[ { "id": "authors:v9n1t-12g44", "collection": "authors", "collection_id": "v9n1t-12g44", "cite_using_url": "https://authors.library.caltech.edu/records/v9n1t-12g44", "type": "book_section", "title": "Sparse Arrays: Fundamentals", "book_title": "Sparse Arrays for Radar, Sonar, and Communications", "author": [ { "family_name": "Vaidyanathan", "given_name": "Palghat P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Kulkarni", "given_name": "Pranav", "clpid": "Kulkarni-Pranav" } ], "editor": [ { "family_name": "Amin", "given_name": "Mmoeness G.", "orcid": "0000-0002-0926-4120", "clpid": "Amin-Moeness-G" } ], "abstract": "
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This chapter is an introduction to sparse arrays. It begins by reviewing the basics of Array Signal Processing. Sparse arrays are then introduced and their advantages explained. A typical application of sensor arrays is in determination of the angles of arrival of different sources from various directions in space. One of the main advantages of sparse arrays is that, under some conditions, they can identify more number of sources than the number of sensors in the array. This unique property is explained using the notion of a difference coarray, and is valid under the assumption that the impinging sources are uncorrelated. A well\u2010designed sparse array has a difference coarray with many more consecutive elements than the number of sensors and this is one of the key properties which makes sparse arrays special. The chapter not only discusses recent sparse arrays such as nested and coprime arrays, but also reviews classical sparse arrays such as minimum redundancy arrays and Golomb rulers. The use of certain classes of sparse arrays in beamforming applications is also elaborated.
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", "doi": "10.1002/9781394191048.ch1", "isbn": "9781394191031", "publisher": "Wiley-IEEE Press", "place_of_publication": "Hoboken, NJ", "publication_date": "2023-12-15", "pages": "1-40" }, { "id": "authors:7ke84-a8m36", "collection": "authors", "collection_id": "7ke84-a8m36", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230526-662994000.10", "type": "book_section", "title": "Difference Coarrays of Rational Arrays", "book_title": "2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Kulkarni", "given_name": "Pranav", "orcid": "0000-0002-1461-0948", "clpid": "Kulkarni-Pranav-D" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Rational arrays were recently proposed for direction of arrival (DOA) estimation, and some of their advantages were discussed. In this paper we discuss further advantages of rational arrays, by considering their difference coarrays. Although integer arrays such as nested arrays, and coprime arrays are well-known for their ability to identify O (m\u00b2) uncorrelated sources using m sensors through difference coarray domain, they can do so only when a large enough aperture is available. However, rational arrays can do so even when the aperture is constrained. We demonstrate that adding a few sensors at non-integer locations in an otherwise integer array can add a large number of fractional lags at which autocorrelation can be estimated. Appropriately designed sparse integer arrays can also be scaled to produce rational arrays that fit available aperture and have large uniform coarray segments at rational locations. Monte-Carlo simulations are provided to demonstrate the advantages, and practical issues associated with shrinking, such as increased mutual coupling, are discussed.", "doi": "10.1109/icassp49357.2023.10095426", "isbn": "9781728163277", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2023-06" }, { "id": "authors:vb24b-2c898", "collection": "authors", "collection_id": "vb24b-2c898", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230526-663003000.14", "type": "book_section", "title": "Error Analysis of Convolutional Beamspace Algorithms", "book_title": "2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "orcid": "0000-0003-1637-9329", "clpid": "Chen-Po-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Beamspace processing for DOA estimation offers low computational complexity and high DOA resolution. Moreover, unlike classical beamspace methods, convolutional beamspace (CBS) preserves the Vandermonde structure of uniform linear array output, so no additional preparation is needed to apply root-MUSIC. In this paper, theoretical MSE of CBS is given when MUSIC or root-MUSIC is used. Error variance can be derived from the asymptotic probability distribution of the eigenvectors of an average finite-snapshot covariance matrix. Meanwhile, the bias due to the filtered stopband sources is given by first-order perturbation analysis. Known advantages of CBS are confirmed by the MSE analysis. For example, CBS yields smaller MSE for correlated sources than element-space. The theoretical results are verified by simulations.", "doi": "10.1109/icassp49357.2023.10095614", "isbn": "978-1-7281-6327-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2023-06", "pages": "1-5" }, { "id": "authors:qq5v4-bn653", "collection": "authors", "collection_id": "qq5v4-bn653", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230526-662999000.12", "type": "book_section", "title": "Interpolation Filter Model For Ramanujan Subspace Signals", "book_title": "2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Kulkarni", "given_name": "Pranav", "orcid": "0000-0002-1461-0948", "clpid": "Kulkarni-Pranav-D" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Ramanujan sums have been shown to have interesting applications in signal processing. Ramanujan subspaces, Ramanujan dictionaries, and Ramanujan filter banks are useful in representing and denoising discrete-time periodic signals. In this paper, we theoretically investigate an ideal interpolation filter model for Ramanujan subspace signals wherein an expander \u2191 M is followed by the ideal q-th Ramanujan filter C q (e j\u03c9 ). The output space of this interpolation filter is, in general, only a proper subspace of the q-th Ramanujan subspace Sq. For the special case when M and q are coprime, we prove that the output space is the entire Ramanujan subspace. We also discuss a more general form of this model for the representation of periodic signals, which may have a potential application in denoising periodic signals. When M and q are not coprime, we provide a bound on the dimension of the output space of the interpolation filter. For this general case, we also conjecture that the provided bound in fact equals the dimension of the output space.", "doi": "10.1109/icassp49357.2023.10095682", "isbn": "978-1-7281-6327-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2023-06", "pages": "1-5" }, { "id": "authors:dvbds-8p187", "collection": "authors", "collection_id": "dvbds-8p187", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230526-662988000.8", "type": "book_section", "title": "Unitary Esprit for Coprime Arrays", "book_title": "2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "orcid": "0000-0003-1637-9329", "clpid": "Chen-Po-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Coprime arrays are normally used to identify more sources than sensors, using the coarray domain. They can also be used directly in element-space and still have benefits of better accuracy and resolution compared to ULAs. An invariance is buried in each of the two sparse ULAs which constitute a coprime array. In this paper, ESPRIT is applied separately to each ULA to yield a set of residues of DOAs, and residues from the ULAs are paired to resolve DOAs. With unitary ESPRIT, residues are automatically paired in the real and imaginary parts of the eigenvalues of a matrix obtained from outputs of the two ULAs. These eigenvalues are proved to be distinct, so the eigendecomposition is unique. Previous works used traditional ESPRIT for similar application, so the eigenvalues corresponding to each invariance were complex; elaborate steps were taken to pair residues. Advantages of the proposed method are demonstrated by simulations.", "doi": "10.1109/icassp49357.2023.10096262", "isbn": "9781728163277", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2023-06" }, { "id": "authors:qyft3-ev668", "collection": "authors", "collection_id": "qyft3-ev668", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230605-334736000.4", "type": "book_section", "title": "Rational Arrays for DOA Estimation: New Insights and Performance Evaluation", "book_title": "2022 56th Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Kulkarni", "given_name": "Pranav", "orcid": "0000-0002-1461-0948", "clpid": "Kulkarni-Pranav-D" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Rational arrays were recently proposed for direction of arrival (DOA) estimation. In particular, rational coprime arrays were demonstrated to be useful when the aperture and the number of sensors are constrained. In this paper, we provide a necessary and sufficient condition for steering vector invertibility of a general rational array. We demonstrate that shrunk rational ULAs can have smaller MSE than integer ULAs when multiple sources impinge from the directions away from the normal to the array. We also propose a new way for generating rational arrays which readily ensures the \"rational coprimality condition\" for identifiability. Arrays generated according to this new way provide better DOA estimation performance compared to pre-viously used rational coprime arrays. Next, the paper provides a detailed performance evaluation for rational coprime arrays in terms of numerical and analytical mean square errors with root-MUSIC. For this, a modification of root-MUSIC for search-free estimation of DOAs with rational arrays is introduced. It is found that rational coprime arrays have smaller MSE than three possible integer arrays with the same aperture and number of sensors, including ULAs and integer coprime arrays.", "doi": "10.1109/ieeeconf56349.2022.10051963", "isbn": "978-1-6654-5906-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2022-11", "pages": "91-95" }, { "id": "authors:8q2r4-bza77", "collection": "authors", "collection_id": "8q2r4-bza77", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230605-334731000.3", "type": "book_section", "title": "Hybrid Convolutional Beamspace for DOA Estimation of Millimeter Wave Sources", "book_title": "2022 56th Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "orcid": "0000-0003-1637-9329", "clpid": "Chen-Po-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Sensor arrays designed for millimeter waves (mmWaves) have gained popularity recently for their potential to offer more bandwidth. To reduce hardware cost, mmWave processing is divided into analog and digital domains. The analog combiner serves as a beamspace processor, reducing the number of required RF chains. Convolutional beamspace (CBS) is a recently proposed beamspace method. It achieves lower computational complexity, higher DOA resolution, and smaller MSE for correlated sources. In this paper, hybrid analog and digital CBS is proposed for DOA estimation of mmWave sources using a receiver array. Constant-modulus constraints imposed on the analog combiner are tackled by the fact that any complex vector is a linear combination of two vectors with unit-modulus entries. The required number of RF chains equals the dimension of the CBS output after decimation. Besides traditional CBS with uniform decimation, a new form with nonuniform decimation is presented. The retained samples correspond to sensor locations of a virtual dilated sparse array. The coarray method then enables the estimation of O(R\u00b2) sources, where R is the number of RF chains. The dilation results in larger coarray aperture and smaller estimation errors. Numerical examples are given to show the effectiveness of hybrid CBS.", "doi": "10.1109/ieeeconf56349.2022.10051878", "isbn": "9781665459068", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2022-11", "pages": "86-90" }, { "id": "authors:ngdy7-k7708", "collection": "authors", "collection_id": "ngdy7-k7708", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220624-4393200", "type": "book_section", "title": "Convolutional Beamspace Using IIR Filters", "book_title": "2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2022)", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "orcid": "0000-0003-1637-9329", "clpid": "Chen-Po-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The recently introduced convolutional beamspace (CBS) method has some advantages over traditional beamspace methods in array processing. This paper introduces a variant which uses IIR instead of FIR filters in the convolutional layer. In CBS, the sources falling in the stopband are assumed to be sufficiently attenuated so that we can identify the pass-band DOAs. An IIR filter often requires a much lower order for the same set of magnitude response specifications. Hence, the computational complexity of IIR-CBS can be smaller than FIR-CBS. Moreover, IIR-CBS can even give smaller DOA estimation errors than FIR-CBS because the longer FIR filter length means shorter steady-state filter output length, which leads to larger estimation errors. The advantages of IIR-CBS are verified by numerical examples.", "doi": "10.1109/icassp43922.2022.9746961", "isbn": "978-1-6654-0540-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2022-05-23", "pages": "5003-5007" }, { "id": "authors:76b3w-qvv98", "collection": "authors", "collection_id": "76b3w-qvv98", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220624-170739742", "type": "book_section", "title": "Rational Arrays for DOA Estimation", "book_title": "2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2022)", "author": [ { "family_name": "Kulkarni", "given_name": "Pranav", "orcid": "0000-0002-1461-0948", "clpid": "Kulkarni-Pranav-D" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Linear arrays used in array processing usually have sensor positions r_i\u03bb/2 where \u03bb is the wavelength of the impinging signals and r_i are integers. This paper considers rational arrays, where r_i are rational numbers. In particular, sparse rational arrays such as coprime rational arrays are introduced. In order to do this, some rational extensions of integer number theoretic concepts such as greatest common divisor and coprime numbers are required, which are introduced as well. The advantages of rational arrays are demonstrated with the help of rational coprime arrays. For example, they improve the accuracy of DOA estimation when the sensors have to be distributed with a fixed aperture constraint.", "doi": "10.1109/ICASSP43922.2022.9746954", "isbn": "978-1-6654-0540-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2022-05-23", "pages": "5008-5012" }, { "id": "authors:8gkdr-sdp22", "collection": "authors", "collection_id": "8gkdr-sdp22", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220317-376205000", "type": "book_section", "title": "Rank Properties of Manifold Matrices of Sparse Arrays", "book_title": "2021 55th Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "orcid": "0000-0003-1637-9329", "clpid": "Chen-Po-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "It is well known that the manifold matrix of a sensor array has to satisfy certain rank conditions in order for certain algorithms such as MUSIC and ESPRIT to work without creating ambiguity. For the case of sparse arrays this condition is often not satisfied, although there exist some sparse arrays which satisfy them. This paper develops the constraints on the sensor locations which allow such conditions to be satisfied. After a number of examples to develop insights, two results are given: one is a necessary and sufficient condition for two specific cases and the other is a necessary condition for the general case. The necessary condition for the general case reduces to the necessary and sufficient condition in the two specific cases. In order for sparse arrays to satisfy these conditions, it is not required that there be a uniform linear subarray with more sensors than sources.", "doi": "10.1109/ieeeconf53345.2021.9723150", "isbn": "978-1-6654-5828-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2021-11", "pages": "1628-1633" }, { "id": "authors:ny4dc-9mk62", "collection": "authors", "collection_id": "ny4dc-9mk62", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220317-376187000", "type": "book_section", "title": "Feature Engineering for DOA Estimation using a Convolutional Neural Network, for Sparse Arrays", "book_title": "2021 55th Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Kulkarni", "given_name": "Pranav", "orcid": "0000-0002-1461-0948", "clpid": "Kulkarni-Pranav-D" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In the past few years, there has been an emerging use of deep neural networks for improving the direction of arrival (DOA) estimation performance. This paper demonstrates how such methods can be applied for sparse arrays such as nested arrays, by adapting a recent method based on convolutional neural network (CNN). Many possible alternative inputs (proxy spectra) to the network are suggested here, and experiments show that even simple modifications of the input lead to improved DOA estimation performance without changing the network structure. Additionally, the experiments also show that, with the modified input proxy spectra it is possible to identify more sources than the number of physical sensors, as one would expect with nested arrays. This opens up further avenues of using coarray principles in conjunction with machine learning methods.", "doi": "10.1109/ieeeconf53345.2021.9723112", "isbn": "978-1-6654-5828-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2021-11", "pages": "246-250" }, { "id": "authors:a2nbn-z7f15", "collection": "authors", "collection_id": "a2nbn-z7f15", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220317-376249000", "type": "book_section", "title": "Distributed Root-MUSIC Using Finite-Time Average Consensus", "book_title": "2021 55th Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "orcid": "0000-0003-1637-9329", "clpid": "Chen-Po-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Distributed (decentralized) algorithms for principal component analysis of covariance matrices are well-known, and their applications in array signal processing have received more interest recently. Inspired by this, a new distributed algorithm for the popular DOA estimation method, root-MUSIC, is proposed. The average consensus method is used to avoid the need for a fusion center in a sensor network, which makes the proposed algorithm fully distributed. In particular, the algorithm is based on a recently reported finite-time version of average consensus which converges to the exact solution in a finite number of iterations. This allows the proposed distributed root-MUSIC to achieve exactly the same performance as the centralized counterpart. The good performance of the proposed algorithm is verified by simulations.", "doi": "10.1109/ieeeconf53345.2021.9723302", "isbn": "978-1-6654-5828-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2021-11", "pages": "539-543" }, { "id": "authors:3vvew-bwn39", "collection": "authors", "collection_id": "3vvew-bwn39", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220317-376196000", "type": "book_section", "title": "Unifying Random-Asynchronous Algorithms for Numerical Methods, Using Switching Systems Theory", "book_title": "2021 55th Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-Oguzhan" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Randomized variants of iterative techniques such as Kaczmarz method, Gauss-Seidel method and asynchronous fixed-point iterations have been of interest in recent years. Due to their randomized nature, these techniques are better suited for processing of large scale and distributed data. Despite their effectiveness, their theoretical analysis has been of interest only in recent years. In the mean-time, control theory literature has studied switching systems rigorously in order to understand the behavior of systems whose dynamics change over time. This paper shows that randomized iterative algorithms can be represented as switching systems. Thus, convergence properties of such randomized algorithms follow directly from the stability theory already developed for switching systems. As an example, alternative proofs are provided for the mean-squared and almost sure convergence of randomized Kaczmarz and Gauss-Seidel methods. The necessary and sufficient condition for the mean-squared convergence of random asynchronous fixed-point iterations is also provided.", "doi": "10.1109/ieeeconf53345.2021.9723385", "isbn": "978-1-6654-5828-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2021-11", "pages": "172-176" }, { "id": "authors:vnga6-cba97", "collection": "authors", "collection_id": "vnga6-cba97", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210601-150636010", "type": "book_section", "title": "Sliding-Capon Based Convolutional Beamspace for Linear Arrays", "book_title": "2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "orcid": "0000-0003-1637-9329", "clpid": "Chen-Po-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "A new method to design the filter for convolutional beamspace (CBS), called Capon-CBS, is proposed. The idea is to design the filter to be a sliding Capon beamformer. Such design takes input statistics into account, so it can do a better job of suppressing the sources that fall in the stopband. Capon-CBS can offer higher probability of resolution and smaller mean square error for DOA estimation, as demonstrated in the simulations. Moreover, like traditional CBS, Capon-CBS also has the advantage of low computational complexity.", "doi": "10.1109/icassp39728.2021.9414022", "isbn": "9781728176055", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2021-06-06", "pages": "4565-4569" }, { "id": "authors:60n81-2kf79", "collection": "authors", "collection_id": "60n81-2kf79", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210602-093734579", "type": "book_section", "title": "Periodic Signal Denoising: An Analysis-Synthesis Framework Based on Ramanujan Filter Banks and Dictionaries", "book_title": "2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Kulkarni", "given_name": "Pranav", "orcid": "0000-0002-1461-0948", "clpid": "Kulkarni-Pranav-D" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Ramanujan filter banks (RFB) have in the past been used to identify periodicities in data. These are analysis filter banks with no synthesis counterpart for perfect reconstruction of the original signal, so they have not been useful for denoising periodic signals. This paper proposes to use a hybrid analysis-synthesis framework for denoising discrete-time periodic signals. The synthesis occurs via a pruned dictionary designed based on the output energies of the RFB analysis filters. A unique property of the framework is that the denoised output signal is guaranteed to be periodic unlike any of the other methods. For a large range of input noise levels, the proposed approach achieves a stable and high SNR gain outperforming many traditional denoising techniques.", "doi": "10.1109/ICASSP39728.2021.9413689", "isbn": "9781728176055", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2021-06-06", "pages": "5100-5104" }, { "id": "authors:1vtyr-n7s41", "collection": "authors", "collection_id": "1vtyr-n7s41", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210622-215812982", "type": "book_section", "title": "Convolutional Beamspace and Sparse Signal Recovery for Linear Arrays", "book_title": "2020 54th Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "orcid": "0000-0003-1637-9329", "clpid": "Chen-Po-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The convolutional beamspace (CBS) method for DOA estimation using dictionary-based sparse signal recovery is introduced. Beamspace methods enjoy lower computational complexity, increased parallelism of subband processing, and improved DOA resolution. But unlike classical beamspace methods, CBS allows root-MUSIC and ESPRIT to be performed directly for ULAs without additional preparation since the Vandermonde structure for ULAs are preserved in the CBS output. Due to the same reason, it is shown in this paper that sparse signal representation problems can also be directly formulated on the CBS output. Significant reduction in computational complexity and higher probability of resolution are obtained by using CBS. It is also shown how the regularization parameter involved in the method should be chosen.", "doi": "10.1109/IEEECONF51394.2020.9443522", "isbn": "978-0-7381-3126-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2020-11", "pages": "929-933" }, { "id": "authors:pqmp2-ks758", "collection": "authors", "collection_id": "pqmp2-ks758", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210622-213746336", "type": "book_section", "title": "K-SVD based Periodicity Dictionary Learning", "book_title": "2020 54th Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Kulkarni", "given_name": "Pranav", "orcid": "0000-0002-1461-0948", "clpid": "Kulkarni-Pranav-D" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "It has recently been shown that periodicity in discrete-time data can be analyzed using Ramanujan sums and associated dictionaries. This paper explores the role of dictionary learning methods in the context of period estimation and periodic signal representation using dictionaries. It is shown that a well-known dictionary learning algorithm, namely K-SVD, is able to learn Ramanujan and Farey periodicity dictionaries from the noisy, sparse coefficient data generated from them without imposing any periodicity structure in the learning stage. This similarity between the learned dictionary and the underlying original periodicity dictionary reaffirms the power of the K-SVD in predicting the right dictionary from data without explicit application-specific constraints. The paper also examines how the choice of different parameter values affect the similarity of the learned dictionary to the underlying dictionary. Two versions of K-SVD along with different initializations are analyzed for their effect on representation and denoising error for the data.", "doi": "10.1109/IEEECONF51394.2020.9443567", "isbn": "978-0-7381-3126-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2020-11", "pages": "1333-1337" }, { "id": "authors:d6k42-b5246", "collection": "authors", "collection_id": "d6k42-b5246", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210622-214927867", "type": "book_section", "title": "Node-Asynchronous Implementation of Filter Banks on Graphs", "book_title": "2020 54th Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-Oguzhan" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Filter banks on graphs are shown to be useful for analyzing data defined over networks, as they decompose a graph signal into components with low variation and high variation. Based on recent node-asynchronous implementation of graph filters, this study proposes an asynchronous implementation of filter banks on graphs. In the proposed algorithm nodes follow a randomized collect-compute-broadcast scheme: if a node is in the passive stage it collects the data sent by its incoming neighbors and stores only the most recent data. When a node gets into the active stage at a random time instance, it does the necessary filtering computations locally, and broadcasts a state vector to its outgoing neighbors. When the underlying filters (of the filter bank) are rational functions with the same denominator, the proposed filter bank implementation does not require additional communication between the neighboring nodes. However, computations done by a node increase linearly with the number of filters in the bank. It is also proven that the proposed asynchronous implementation converges to the desired output of the filter bank in the mean-squared sense under mild stability conditions. The convergence is verified also with numerical experiments.", "doi": "10.1109/IEEECONF51394.2020.9443349", "isbn": "978-0-7381-3126-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2020-11", "pages": "460-464" }, { "id": "authors:e5jf3-msx61", "collection": "authors", "collection_id": "e5jf3-msx61", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200417-140311291", "type": "book_section", "title": "Node-Asynchronous Spectral Clustering On Directed Graphs", "book_title": "2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In recent years the convergence behavior of random node asynchronous graph communications have been studied for the case of undirected graphs. This paper extends these results to the case of graphs having arbitrary directed edges possibly with a nondiagonalizable adjacency matrix. Assuming that the graph operator has eigenvalue 1 and the input signal satisfies a certain condition (which ensures the existence of fixed points), this study presents the necessary and sufficient condition for the mean-squared convergence of the graph signal. The presented condition depends on the graph operator as well as the update probabilities, and the convergence of the randomized asynchronous updates may be achieved even when the underlying operator is not stable in the synchronous setting. As an application, the node-asynchronous updates are combined with polynomial filtering in order to obtain a spectral clustering for directed networks. The convergence is also verified with numerical simulations.", "doi": "10.1109/ICASSP40776.2020.9054241", "isbn": "9781509066315", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2020-05", "pages": "5325-5329" }, { "id": "authors:nsvd8-8t219", "collection": "authors", "collection_id": "nsvd8-8t219", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200417-132226845", "type": "book_section", "title": "Convolutional Beamspace for Array Signal Processing", "book_title": "2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Chen", "given_name": "Po-Chih", "clpid": "Chen-Po-Chih" } ], "abstract": "A new type of beamspace for array processing is introduced called convolutional beamspace. It enjoys the advantages of traditional beamspace such as lower computational complexity, increased parallelism of subband processing, and improved resolution threshold for DOA estimation. But unlike traditional beamspace methods, it allows root-MUSIC and ESPRIT to be performed directly for ULAs without any overhead of preparation, as the Vandermonde structure and the shift-invariance are preserved under the transformation. The method produces more accurate DOA estimates than traditional beamspace methods, and for correlated sources it produces better estimates than element-space methods.", "doi": "10.1109/ICASSP40776.2020.9054051", "isbn": "9781509066315", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2020-05", "pages": "4707-4711" }, { "id": "authors:ewhqf-b1g46", "collection": "authors", "collection_id": "ewhqf-b1g46", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210304-101834311", "type": "book_section", "title": "One-Bit Normalized Scatter Matrix Estimation For Complex Elliptically Symmetric Distributions", "book_title": "2020 IEEE International Conference on Acoustics, Speech and Signal Processing", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "One-bit quantization has attracted attention in massive MIMO, radar, and array processing, due to its simplicity, low cost, and capability of parameter estimation. Specifically, the shape of the covariance of the unquantized data can be estimated from the arcsine law and onebit data, if the unquantized data is Gaussian. However, in practice, the Gaussian assumption is not satisfied due to outliers. It is known from the literature that outliers can be modeled by complex elliptically symmetric (CES) distributions with heavy tails. This paper shows that the arcsine law remains applicable to CES distributions. Therefore, the normalized scatter matrix of the unquantized data can be readily estimated from one-bit samples derived from CES distributions. The proposed estimator is not only computationally fast but also robust to CES distributions with heavy tails. These attributes will be demonstrated through numerical examples, in terms of computational time and the estimation error. An application in DOA estimation with MUSIC spectrum is also presented.", "doi": "10.1109/icassp40776.2020.9053956", "isbn": "9781509066315", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2020-05", "pages": "9130-9134" }, { "id": "authors:p3zkq-h9h78", "collection": "authors", "collection_id": "p3zkq-h9h78", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200402-145101457", "type": "book_section", "title": "Randomized Asynchronous Recursions with a Sinusoidal Input", "book_title": "2019 53rd Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This study considers a randomized asynchronous form of the discrete time-invariant state-space models, in which only a random subset of the state variables is updated in each iteration. When the system has a single input in the form of a complex exponential, it is shown that the output signal still behaves like an exponential in a statistical sense. The study presents the necessary and sufficient condition that ensures the stability of a randomized asynchronous system, which does not necessarily require the stability of the state transition matrix.", "doi": "10.1109/ieeeconf44664.2019.9048998", "isbn": "9781728143002", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2019-11", "pages": "1491-1495" }, { "id": "authors:kpcp0-tka14", "collection": "authors", "collection_id": "kpcp0-tka14", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200402-144126560", "type": "book_section", "title": "On ESPRIT with Multiple Coprime-Invariances", "book_title": "2019 53rd Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "clpid": "Chen-Po-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In conventional ESPRIT, a single translational invariance in a sensor array is used to obtain high-resolution direction-of-arrival (DOA) estimation. However, when the invariance is greater than the classical sensor spacing \u03bb/2, spatial frequency ambiguity may occur. In this paper, we propose to use multiple setwise coprime invariances to resolve this ambiguity. While special cases of this were known in the literature, our algorithm is more general in that we consider any number of invariances, and that it can perfectly recover any number of DOAs (limited only in terms of number of sensors) if infinite snapshots are available. We also demonstrate through simulation that our algorithm works well in a practical setting where only finite snapshots are available.", "doi": "10.1109/ieeeconf44664.2019.9048797", "isbn": "9781728143002", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2019-11", "pages": "148-152" }, { "id": "authors:87sq7-phy26", "collection": "authors", "collection_id": "87sq7-phy26", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200403-143552815", "type": "book_section", "title": "DSP-Inspired Deep Learning: A Case Study Using Ramanujan Subspaces", "book_title": "2019 53rd Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Can Deep Learning be used to augment DSP techniques? Algorithms in DSP are typically developed starting from a mathematical model of an application. In some cases however, simplicity of the model can result in deterioration of performance when there is a severe modeling mis-match. This paper explores the idea of implementing a DSP technique as a computational graph, so that hundreds of parameters can jointly be trained to adapt to any given dataset. Using the specific example of period estimation by Ramanujan Subspaces, significant improvement in estimation accuracies under high noise and very short datalengths is demonstrated.", "doi": "10.1109/ieeeconf44664.2019.9048783", "isbn": "9781728143002", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2019-11", "pages": "2072-2076" }, { "id": "authors:7arna-tya89", "collection": "authors", "collection_id": "7arna-tya89", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190913-090526091", "type": "book_section", "title": "The random component-wise power method", "book_title": "Wavelets and Sparsity XVIII", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "Palghat P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Van De Ville", "given_name": "Dimitri", "clpid": "Van-De-Ville-D" }, { "family_name": "Papadakis", "given_name": "Manos", "clpid": "Papadakis-M" }, { "family_name": "Lu", "given_name": "Yue M.", "clpid": "Lu-Yue-M" } ], "abstract": "This paper considers a random component-wise variant of the unnormalized power method, which is similar to the regular power iteration except that only a random subset of indices is updated in each iteration. For the case of normal matrices, it was previously shown that random component-wise updates converge in the mean-squared sense to an eigenvector of eigenvalue 1 of the underlying matrix even in the case of the matrix having spectral radius larger than unity. In addition to the enlarged convergence regions, this study shows that the eigenvalue gap does not directly affect the convergence rate of the randomized updates unlike the regular power method. In particular, it is shown that the rate of convergence is affected by the phase of the eigenvalues in the case of random component-wise updates, and the randomized updates favor negative eigenvalues over positive ones. As an application, this study considers a reformulation of the component-wise updates revealing a randomized algorithm that is proven to converge to the dominant left and right singular vectors of a normalized data matrix. The algorithm is also extended to handle large-scale distributed data when computing an arbitrary rank approximation of an arbitrary data matrix. Numerical simulations verify the convergence of the proposed algorithms under different parameter settings.", "doi": "10.1117/12.2530511", "isbn": "9781510629691", "publisher": "Society of Photo-Optical Instrumentation Engineers (SPIE)", "place_of_publication": "Bellingham, WA", "publication_date": "2019-09-09", "pages": "Art. No. 111381L" }, { "id": "authors:mvjd3-5cq67", "collection": "authors", "collection_id": "mvjd3-5cq67", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190424-103509340", "type": "book_section", "title": "Composite Singer Arrays with Hole-free Coarrays and Enhanced Robustness", "book_title": "2019 IEEE International Conference on Acoustics, Speech and Signal Processing", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In array processing, minimum redundancy arrays (MRA) can identify up to O(N^2) uncorrelated sources (the O(N^2) property) with N physical sensors, but this property is susceptible to sensor failures. On the other hand, uniform linear arrays (ULA) are robust, but they resolve only O(N) sources. Recently, the robust MRA (RMRA) was shown to possess the O(N^2) property and to be as robust as ULA. But finding RMRA is computationally difficult for large N. This paper proposes a novel array geometry called the composite Singer array, which is related to a classic paper by Singer in 1938, and to other results in number theory. For large N, composite Singer arrays could own the O(N^2) property and are as robust as ULA. Furthermore, the sensor locations for the composite Singer array can be readily computed by the proposed recursive procedure. These properties will also be demonstrated by using numerical examples.", "doi": "10.1109/ICASSP.2019.8683563", "isbn": "978-1-5386-4658-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2019-05", "pages": "4120-4124" }, { "id": "authors:c46em-wts63", "collection": "authors", "collection_id": "c46em-wts63", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190424-093013122", "type": "book_section", "title": "Node-asynchronous Implementation of Rational Filters on Graphs", "book_title": "2019 IEEE International Conference on Acoustics, Speech and Signal Processing", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper considers a node-asynchronous implementation of rational (\"IIR\") filters on graphs, in which the nodes are assumed to wake up randomly and independently from each other, and communicate only with their immediate neighbors. The underlying graph is allowed to be directed, possibly with a non-diagonalizable adjacency matrix. Since the nodes are allowed to act independently, the proposed implementation is practical for very large or autonomous networks where synchronization is difficult to achieve. Furthermore, the proposed algorithm is 1-hop localized on the graph irrespective of the order of the filter. The method is shown to converge in the mean-squared sense under a boundedness assumption on the filter as well as the graph operator. The result follows from the convergence of a more general randomized asynchronous state recursion, which is also presented in this paper. The algorithm is simulated on a random geometric graph, which numerically verifies the convergence.", "doi": "10.1109/ICASSP.2019.8682946", "isbn": "978-1-5386-4658-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2019-05", "pages": "7530-7534" }, { "id": "authors:0v50y-m8t33", "collection": "authors", "collection_id": "0v50y-m8t33", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190228-154232324", "type": "book_section", "title": "Energy Compaction Filters on Graphs", "book_title": "2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In classical signal processing spectral concentration is an important problem that was first formulated and analyzed by Slepian. The solution to this problem gives the optimal FIR filter that can confine the largest amount of energy in a specific bandwidth for a given filter order. The solution is also known as the prolate sequence. This study investigates the same problem for polynomial graph filters. The problem is formulated in both graph-free and graph-dependent fashions. The graph-free formulation assumes a continuous graph spectrum, in which case it becomes the polynomial concentration problem. This formulation has a universal approach that provides a theoretical reference point. However, in reality graphs have discrete spectrum. The graph-dependent formulation assumes that the eigenvalues of the graph are known and formulates the energy compaction problem accordingly. When the eigenvalues of the graph have a uniform distribution, the graph-dependent formulation is shown to be asymptotically equivalent to the graph-free formulation. However, in reality eigenvalues of a graph tend to have different densities across the spectrum. Thus, the optimal filter depends on the underlying graph operator, and a filter cannot be universally optimal for every graph.", "doi": "10.1109/GlobalSIP.2018.8646570", "isbn": "978-1-7281-1295-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-11", "pages": "783-787" }, { "id": "authors:m56g8-afp33", "collection": "authors", "collection_id": "m56g8-afp33", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190301-154838714", "type": "book_section", "title": "Asynchronous Nonlinear Updates on Graphs", "book_title": "52nd Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The notion of graph shift, introduced recently in graph signal processing, extends many classical signal processing techniques to graphs. Its practical importance follows from its localization: a single graph shift requires nodes to communicate only with their neighbors. However, communications should happen simultaneously, which requires a synchronization over the graph. In order to overcome this restriction, recent studies consider a random asynchronous variant of the graph shift, which is also suitable for autonomous networks. A graph signal under this randomized scheme is shown to converge (under mild conditions) to an eigenvector of the eigenvalue 1 of the operator even if the operator has other eigenvalues with magnitudes larger than unity. If the eigenvalue 1 does not exist, the operator can be easily normalized in theory. However, in practice, the normalization requires one to know the (dominant) eigenvalues, which may not be possible to obtain in large autonomous networks. To eliminate this limitation, this study considers the use of a nonlinearity in the updates making the scheme similar in spirit to the Hopfield neural network model. Our simulation results show that a graph signal still approaches the eigenvector of the dominant eigenvalue although the convergence is not exact. Nevertheless, approximation is sufficient to accomplish certain tasks including autonomous clustering.", "doi": "10.1109/ACSSC.2018.8645351", "isbn": "978-1-5386-9218-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-10", "pages": "998-1002" }, { "id": "authors:vhan8-2m086", "collection": "authors", "collection_id": "vhan8-2m086", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190301-152543153", "type": "book_section", "title": "Absence Seizure Detection Using Ramanujan Filter Banks", "book_title": "52nd Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Absence seizures are a type of generalized seizures characterized by a 3 Hz periodic spike and wave discharge pattern in the Electroencephalogram (EEG). The most common way to diagnose them is by detecting such periodic patterns in a patient's EEG. Recently, a new method known as Ramanujan Filter Bank (RFB) was proposed for identifying, estimating and localizing periodicities in data. The RFB was shown to offer important advantages over traditional period estimation techniques in DSP. In this work, we demonstrate that the RFB offers very useful diagnostic information when applied to EEG signals from absence-seizure patients.", "doi": "10.1109/ACSSC.2018.8645492", "isbn": "978-1-5386-9218-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-10", "pages": "1913-1917" }, { "id": "authors:pr0y1-z5k66", "collection": "authors", "collection_id": "pr0y1-z5k66", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190301-155512046", "type": "book_section", "title": "Minimal Non-Uniform Sampling For Multi-Dimensional Period Identification", "book_title": "52nd Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper addresses a fundamental question in the context of multi-dimensional periodicity. Namely, to distinguish between two N-dimensional periodic patterns, what is the least number of (possibly non-contiguous) samples that need to be observed? This question was only recently addressed for one-dimensional signals. This paper generalizes those results to N-dimensional signals. It will be shown that the optimal sampling pattern takes the form of sparse and uniformly separated bunches. Apart from new theoretical insights, this paper's results may provide the foundation for fast N-dimensional period recognition algorithms that use minimal number of samples.", "doi": "10.1109/ACSSC.2018.8645347", "isbn": "978-1-5386-9218-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-10", "pages": "2104-2108" }, { "id": "authors:5qp96-phn05", "collection": "authors", "collection_id": "5qp96-phn05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190301-153800720", "type": "book_section", "title": "Optimizing Minimum Redundancy Arrays for Robustness", "book_title": "52nd Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Sparse arrays have received considerable attention due to their capability of resolving O(N^2)uncorrelated sources with N physical sensors, unlike the uniform linear array (ULA) which identifies at most N\u22121 sources. This is because sparse arrays have an O(N^2)\u2212long ULA segment in the difference coarray, defined as the set of differences between sensor locations. Among the existing array configurations, minimum redundancy arrays (MRA) have the largest ULA segment in the difference coarray with no holes. However, in practice, ULA is robust, in the sense of coarray invariance to sensor failure, but MRA is not. This paper proposes a novel array geometry, named as the robust MRA (RMRA), that maximizes the size of the hole-free difference coarray subject to the same level of robustness as ULA. The RMRA can be found by solving an integer program, which is computationally expensive. Even so, it will be shown that the RMRA still owns O(N^2) elements in the hole-free difference coarray. In particular, for sufficiently large N, the aperture for RMRA, which is approximately half of the size of the difference coarray, is bounded between 0.0625N^2 and 0.2174N^2.", "doi": "10.1109/ACSSC.2018.8645482", "isbn": "978-1-5386-9218-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-10", "pages": "79-83" }, { "id": "authors:ytphh-3y451", "collection": "authors", "collection_id": "ytphh-3y451", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180906-142258359", "type": "book_section", "title": "Comparison of Sparse Arrays From Viewpoint of Coarray Stability and Robustness", "book_title": "2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM)", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Sparse arrays, such as minimum redundancy arrays (MRA), nested arrays, and coprime arrays, can resolve O(N^2), uncorrelated sources with N physical sensors, since they possess an O(N2) -long uniform segment in the difference coarray, which is defined as the differences between sensor locations. Empirically, this O(N^2), property is susceptible to sensor failures. On the other hand, uniform linear arrays (ULA) are known to be robust, but they possess only O(N) elements in the difference coarray. This paper compares the size and the robustness of the difference coarray for a wide variety of array geometries. It is observed from numerical examples that, for a fixed N, increasing the size of the difference coarray typically makes it less robust to faulty sensors. Furthermore, it is noticed from examples that given two arrays with the same N and the same difference coarray, one could be much more robust than the other.", "doi": "10.1109/SAM.2018.8448465", "isbn": "978-1-5386-4752-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-07", "pages": "36-40" }, { "id": "authors:ec5e0-y1887", "collection": "authors", "collection_id": "ec5e0-y1887", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180920-110813089", "type": "book_section", "title": "The Asynchronous Power Iteration: A Graph Signal Perspective", "book_title": "2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper considers an autonomous network in which the nodes communicate only with their neighbors at random time instances, repeatedly and independently. Polynomial graph filters studied in the context of graph signal processing are inadequate to analyze signals on this type of networks. This is due to the fact that the basic shift on a graph requires all the nodes to communicate at the same time, which cannot be assumed in an autonomous setting. In order to analyze these type of networks, this paper studies an asynchronous power iteration that updates the values of only a subset of nodes. This paper further reveals the close connection between asynchronous updates and the notion of smooth signals on the graph. The paper also shows that a cascade of random asynchronous updates smooths out any arbitrary signal on the graph.", "doi": "10.1109/ICASSP.2018.8461872", "isbn": "978-1-5386-4658-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-04", "pages": "4059-4063" }, { "id": "authors:tedjz-d2155", "collection": "authors", "collection_id": "tedjz-d2155", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181025-113900814", "type": "book_section", "title": "When Does Periodicity in Discrete-Time Imply that in Continuous-Time?", "book_title": "2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tenneti", "given_name": "Srikanth", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" } ], "abstract": "If the sampled version x(n)=x_c(nT) of a continuous-time signal x_c(t) is periodic, it does not necessarily imply that x_c(t) is periodic. This paper presents some conditions under which periodicity of x_c(t) is indeed implied. The conditions for this implication are more relaxed than bandlimitedness. The results place in evidence a multriate method to estimate the period of x_c(t) from the samples x(n). The method works better than DFT based methods when the available data segment is short and multiple hidden periods are to be estimated.", "doi": "10.1109/ICASSP.2018.8461996", "isbn": "978-1-5386-4658-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-04", "pages": "4544-4548" }, { "id": "authors:yzch4-gym35", "collection": "authors", "collection_id": "yzch4-gym35", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180920-112433763", "type": "book_section", "title": "Robustness of Coarrays of Sparse Arrays to Sensor Failures", "book_title": "2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Sparse arrays can identify O(N^2) uncorrelated sources using N physical sensors. This property is because the difference coarray, defined as the differences between sensor locations, has uniform linear array (ULA) segments of length O(N^2) . It is empirically known that, for sparse arrays like minimum redundancy arrays, nested arrays, and coprime arrays, this O(N^2) segment is susceptible to sensor failure, which is an important issue in practical systems. This paper presents the (k-)essentialness property, which characterizes the combinations of the failing sensors that shrink the difference coarray. Based on this, the notion of fragility is proposed to quantify the reliability of sparse arrays with faulty sensors, along with comprehensive studies of their properties. It is demonstrated through examples that there do exist sparse arrays that are as robust as ULA and at the same time, they enjoy O(N^2) consecutive elements in the difference coarray.", "doi": "10.1109/ICASSP.2018.8462643", "isbn": "978-1-5386-4658-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-04", "pages": "3231-3235" }, { "id": "authors:h9dr5-7a306", "collection": "authors", "collection_id": "h9dr5-7a306", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180419-082338809", "type": "book_section", "title": "Maximally economic sparse arrays and Cantor arrays", "book_title": "2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Sparse arrays, where the sensors are properly placed with nonuniform spacing, are able to resolve more uncorrelated sources than sensors. This ability arises from the property that the difference coarray, defined as the differences between sensor locations, has many more consecutive integers (hole-free) than the number of sensors. In some implementations, it might be preferable that a) the arrays be symmetric, b) that the arrays be maximally economic, that is, each sensor be essential, and c) that the coarray be hole-free. The essentialness property of a sensor means that if it is deleted, then the difference coarray changes. Existing sparse arrays, such as minimum redundancy arrays (MRA), nested arrays, and coprime arrays do not satisfy these three criteria simultaneously. It will be shown in this paper that Cantor arrays meet all the desired properties mentioned above, based on a comprehensive study on the structure of the difference coarray. Even though Cantor arrays were previously proposed in fractal array design, their coarray properties have not been studied earlier. It will also be shown that the Cantor array has a hole-free difference coarray of size N^(log_2^3) \u2248 N^(1.585) where N is the number of sensors. This is unlike the sizes of difference coarrays of the MRA, nested array, coprime array (all O(N^2)), and uniform linear arrays (O(N))^1.", "doi": "10.1109/CAMSAP.2017.8313139", "isbn": "978-1-5386-1251-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2017-12", "pages": "1-5" }, { "id": "authors:7wg09-jyb70", "collection": "authors", "collection_id": "7wg09-jyb70", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180419-095825149", "type": "book_section", "title": "The role of difference coarrays in correlation subspaces", "book_title": "2017 51st Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The concept of correlation subspaces was recently introduced in array processing literature by Rahmani and Atia. Given a sensor array, its geometry determines the correlation subspace completely, and the covariance matrix of the array output is constrained in a certain way by the correlation subspace. It has been shown by Rahmani and Atia that this knowledge about the covariance constraint can be exploited to improve the performance of DOA estimators. In this paper, it is shown that there is a simple closed form expression for the basis vectors of the correlation subspace. Thus, computation of this subspace is greatly simplified. Another fundamental observation is that, this expression is closely related to the difference coarray. Thirdly, the paper also shows an interesting logical connection between correlation subspaces, redundancy averaging, and rectification, which are popularly used in DOA estimation.", "doi": "10.1109/ACSSC.2017.8335536", "isbn": "978-1-5386-1823-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2017-11", "pages": "1173-1177" }, { "id": "authors:2kmtd-4jq72", "collection": "authors", "collection_id": "2kmtd-4jq72", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180419-095409264", "type": "book_section", "title": "Time estimation for heat diffusion on graphs", "book_title": "2017 51st Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper studies the estimation of the starting time of a diffusion process from its noisy measurements when there is a single point source located on a known vertex of a graph with unknown starting time. The diffusion process is assumed to be governed by the heat equation. In particular, the Cramer-Rao lower bound (CRLB) for the problem is derived. It is shown that the problem has a larger CRLB for graphs with higher connectivity. Closed form expression of the bound is derived for some graphs. The ML estimator is numerically verified to be unbiased, and achieve the CRLB for some graphs.", "doi": "10.1109/ACSSC.2017.8335709", "isbn": "978-1-5386-1823-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2017-11", "pages": "1963-1967" }, { "id": "authors:b2my0-qn212", "collection": "authors", "collection_id": "b2my0-qn212", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180419-095014777", "type": "book_section", "title": "MUSIC and Ramanujan: MUSIC-like algorithms for integer periods using nested-periodic-subspaces", "book_title": "2017 51st Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Can the MUSIC algorithm be used for period estimation? Prior works in this direction were based on modifying the search over the conventional complex-exponentials based pseudospectrum to look for harmonically spaced peaks. For applications where the period of the discrete signal can be well approximated by integers, this paper proposes much simpler integer valued basis functions. It is shown that this new re-formulation of MUSIC not only makes the pseudo-spectrum computation much simpler, but also offers significantly higher accuracy than the conventional techniques, especially for mixtures of periodic signals.", "doi": "10.1109/ACSSC.2017.8335717", "isbn": "978-1-5386-1823-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2017-11", "pages": "1997-2001" }, { "id": "authors:8hnp5-6gr76", "collection": "authors", "collection_id": "8hnp5-6gr76", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171220-142223215", "type": "book_section", "title": "Extending classical multirate signal processing theory to graphs", "book_title": "Wavelets and Sparsity XVII", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "Palghat P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Lu", "given_name": "Yue M.", "clpid": "Lu-Yue-M" }, { "family_name": "Van De Ville", "given_name": "Dimitri", "clpid": "Van-De-Ville-D" }, { "family_name": "Papadakis", "given_name": "Manos", "clpid": "Papadakis-M" } ], "abstract": "A variety of different areas consider signals that are defined over graphs. Motivated by the advancements in graph signal processing, this study first reviews some of the recent results on the extension of classical multirate signal processing to graphs. In these results, graphs are allowed to have directed edges. The possibly non-symmetric adjacency matrix A is treated as the graph operator. These results investigate the fundamental concepts for multirate processing of graph signals such as noble identities, aliasing, and perfect reconstruction (PR). It is shown that unless the graph satisfies some conditions, these concepts cannot be extended to graph signals in a simple manner. A structure called M-Block cyclic structure is shown to be sufficient to generalize the results for bipartite graphs on two-channels to M-channel filter banks. Many classical multirate ideas can be extended to graphs due to the unique eigenstructure of M-Block cyclic graphs. For example, the PR condition for filter banks on these graphs is identical to PR in classical theory, which allows the use of well-known filter bank design techniques. In order to utilize these results, the adjacency matrix of an M-Block cyclic graph should be given in the correct permutation. In the final part, this study proposes a spectral technique to identify the hidden M-Block cyclic structure from a graph with noisy edges whose adjacency matrix is given under a random permutation. Numerical simulation results show that the technique can recover the underlying M-Block structure in the presence of random addition and deletion of the edges.", "doi": "10.1117/12.2272362", "isbn": "9781510612457", "publisher": "Society of Photo-Optical Instrumentation Engineers", "place_of_publication": "Bellingham, WA", "publication_date": "2017-08-24", "pages": "Art. No. 103941R" }, { "id": "authors:0jxnh-9k986", "collection": "authors", "collection_id": "0jxnh-9k986", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170621-163606697", "type": "book_section", "title": "Minimum number of possibly non-contiguous samples to distinguish two periods", "book_title": "2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Given that a sequence x(n) is periodic with period P belonging to a known integer set {P_1, P_2, \u2026 P_L}, what is the minimum number of samples of x(n) required to find the period? For the special case where the samples of x(n) are constrained to be contiguous in time, this problem has recently been solved. More generally, when the samples are allowed to be non-contiguous, the problem is quite difficult. This paper provides the answer for the restricted situation where P \u2208 {P_1, P_2}. With P_1 < P_2, the necessary and sufficient number of (possibly noncontiguous) samples for period estimation turns out to be (a) P_1, if P_1 is not a divisor of P_2, and (b) P_2 otherwise. While the proof is quite involved even in this restricted case, it is likely to form the basis for addressing the more general situation where P \u2208 {P_1, P_2, \u2026 P_L}.", "doi": "10.1109/ICASSP.2017.7952872", "isbn": "978-1-5090-4117-6", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2017-03", "pages": "3824-3828" }, { "id": "authors:kyzw5-wyg40", "collection": "authors", "collection_id": "kyzw5-wyg40", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170621-155418409", "type": "book_section", "title": "One-bit sparse array DOA estimation", "book_title": "2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "One-bit quantization has become an important topic in massive MIMO systems, as it offers low cost and low complexity in the implementation. Techniques to achieve high performance in spite of the coarse quantizers have recently been advanced. In the context of array processing and direction-of-arrival (DOA) estimation also, one bit quantizers have been studied in the past, although not as extensively. This paper shows that sparse arrays such as nested and coprime arrays are more robust to the deleterious effects of one-bit quantization, compared to uniform linear arrays (ULAs); in fact, sparse arrays with one-bit quantizers are often found to be as good as ULAs with unquantized data. Nested and coprime arrays without quanitzers are known to be able to resolve more DOAs than the number of sensors, when sources are uncorrelated. It will be demonstrated that this continues to be true even with one-bit quantization.", "doi": "10.1109/ICASSP.2017.7952732", "isbn": "978-1-5090-4117-6", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2017-03", "pages": "3126-3130" }, { "id": "authors:h11tc-kf787", "collection": "authors", "collection_id": "h11tc-kf787", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170621-170410534", "type": "book_section", "title": "Sparse eigenvectors of graphs", "book_title": "2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In order to analyze signals defined over graphs, many concepts from the classical signal processing theory have been extended to the graph case. One of these concepts is the uncertainty principle, which studies the concentration of a signal on a graph and its graph Fourier basis (GFB). An eigenvector of a graph is the most localized signal in the GFB by definition, whereas it may not be localized in the vertex domain. However, if the eigenvector itself is sparse, then it is concentrated in both domains simultaneously. In this regard, this paper studies the necessary and sufficient conditions for the existence of 1, 2, and 3-sparse eigenvectors of the graph Laplacian. The provided conditions are purely algebraic and only use the adjacency information of the graph. Examples of both classical and real-world graphs with sparse eigenvectors are also presented.", "doi": "10.1109/ICASSP.2017.7952888", "isbn": "978-1-5090-4117-6", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2017-03", "pages": "3904-3908" }, { "id": "authors:ebkv2-yzf56", "collection": "authors", "collection_id": "ebkv2-yzf56", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170621-153149358", "type": "book_section", "title": "Efficient multiplier-less structures for Ramanujan filter banks", "book_title": "2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tenneti", "given_name": "Srikanth", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" } ], "abstract": "Ramanujan filter banks (RFB) are useful to generate time-period plane plots which allow one to localize multiple periodic components in the time domain. For such applications, the RFB produces more satisfactory results compared to short time Fourier transforms and other conventional methods, as demonstrated in recent years. This paper introduces a novel multiplier-less, hence computationally very efficient, structure to implement Ramanujan filter banks, based on a new result connecting Ramanujan sums and natural periodic bases.", "doi": "10.1109/ICASSP.2017.7953400", "isbn": "978-1-5090-4117-6", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2017-03", "pages": "6458-6462" }, { "id": "authors:es2bq-0qt56", "collection": "authors", "collection_id": "es2bq-0qt56", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-150012043", "type": "book_section", "title": "Two-Dimensional Sparse Arrays with Hole-Free Coarray and Reduced Mutual Coupling", "book_title": "50th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Two-dimensional sparse arrays with hole-free difference coarrays, like billboard arrays and open box arrays, can identify O(N^2) uncorrelated source directions (DOA) using N sensors. These arrays contain some dense ULA segments, leading to many sensor pairs separated by \u03bb/2. The DOA estimation performance often suffers degradation due to mutual coupling between such closely-spaced sensor pairs. This paper introduces a new 2D array called the half open box array. For a given N, this array has the same hole-free coarray as an open box array. At the same time, the number of sensor pairs with small separation is significantly reduced.", "doi": "10.1109/ACSSC.2016.7869629", "isbn": "978-1-5386-3954-2", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-11", "pages": "1508-1512" }, { "id": "authors:253xd-0d753", "collection": "authors", "collection_id": "253xd-0d753", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170308-162825251", "type": "book_section", "title": "Discrete uncertainty principles on graphs", "book_title": "50th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper advances a new way to formulate the uncertainty principle for graphs, by using a non-local measure based on the notion of sparsity. The uncertainty principle is formulated based on the total number of nonzero elements in the signal and its corresponding graph Fourier transform (GFT). By providing a lower bound for this total number, it is shown that a nonzero graph signal and its GFT cannot be arbitrarily sparse simultaneously. The theoretical bound on total sparsity is derived. For several real-world graphs this bound can actually be achieved by choosing the graph signals to be appropriate eigenvectors of the graph.", "doi": "10.1109/ACSSC.2016.7869622", "isbn": "978-1-5386-3954-2", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-11", "pages": "1475-1479" }, { "id": "authors:586x7-ppp23", "collection": "authors", "collection_id": "586x7-ppp23", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170308-163329746", "type": "book_section", "title": "Detection of protein repeats using the Ramanujan Filter Bank", "book_title": "50th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Protein repeats are tandemly repeating segments within an amino acid sequence. They induce several important structural and binding properties on the protein. So far, the most successful detection schemes for such repeats have used computationally expensive techniques such as dynamic programming algorithms, HMMs, and so on. Classical DSP tools such as STFT, unfortunately, perform poorly in the presence of mutations. In this work, a novel technique is proposed based on the recently developed Ramanujan Filter Bank. Fast, accurate, and involving only simple integer computations, its performance is demonstrated on several well-known repeat families.", "doi": "10.1109/ACSSC.2016.7869058", "isbn": "978-1-5386-3954-2", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-11", "pages": "351-355" }, { "id": "authors:yk9wh-b7r59", "collection": "authors", "collection_id": "yk9wh-b7r59", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160921-132608343", "type": "book_section", "title": "New Cram\u00e9r-Rao bound expressions for coprime and other sparse arrays", "book_title": "2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The Cram\u00e9r-Rao bound (CRB) offers a lower bound on the variances of unbiased estimates of parameters, e.g., directions of arrival (DOA) in array processing. While there exist landmark papers on the study of the CRB in the context of array processing, the closed-form expressions available in the literature are not easy to use in the context of sparse arrays (such as minimum redundancy arrays (MRAs), nested arrays, or coprime arrays) for which the number of identifiable sources D exceeds the number of sensors N. Under such situations, the existing literature does not spell out the conditions under which the Fisher information matrix is nonsingular, or the condition under which specific closed-form expressions for the CRB remain valid. This paper derives a new expression for the CRB to fill this gap. The conditions for validity of this expression are expressed as the rank condition of a matrix defined based on the difference coarray. The rank condition and the closed-form expression lead to a number of new insights. For example, it is possible to prove the previously known experimental observation that, when there are more sources than sensors, the CRB stagnates to a constant value as the SNR tends to infinity.", "doi": "10.1109/SAM.2016.7569620", "isbn": "978-1-5090-2104-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-07", "pages": "1-5" }, { "id": "authors:q424c-55j93", "collection": "authors", "collection_id": "q424c-55j93", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160919-103121476", "type": "book_section", "title": "High Order Super Nested Arrays", "book_title": "2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Mutual coupling between sensors has a negative impact on the estimation of directions of arrival (DOAs). Sparse arrays such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs) have less mutual coupling than uniform linear arrays (ULAs). These sparse arrays also have a difference coarray of size O(N^2), where N is the number of sensors, and can therefore resolve O(N^2) uncorrelated source directions. The various sparse arrays proposed in the literature have their pros and cons. The nested array is practical and easy to use but has a dense ULA part which suffers from mutual coupling effects like the traditional ULA. The recently introduced super nested arrays reduce this mutual coupling problem, while maintaining the desirable hole-free O(N^2) difference coarray of the nested array. In this paper, a generalization of super nested arrays is introduced, called the Qth-order super nested array. This has all the properties of the second-order super nested array with the additional advantage that mutual coupling effects are further reduced for Q > 2. A numerical example is included to demonstrate the superior performance of these arrays.", "doi": "10.1109/SAM.2016.7569621", "isbn": "978-1-5090-2104-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-07", "pages": "1-5" }, { "id": "authors:grr5h-ztg95", "collection": "authors", "collection_id": "grr5h-ztg95", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160823-083839461", "type": "book_section", "title": "Critical data length for period estimation", "book_title": "2016 IEEE International Symposium on Circuits and Systems (ISCAS)", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We address the following question in this paper:\nGiven that the period of a discrete time periodic signal belongs\nto a set P = {P_1, P_2,\u2026,P_K}, what is the minimum duration\nof the signal necessary to identify its period? It will be shown\nthat the following number of samples is both necessary and\nsufficient: max P_i + P_j - gcd(P_i, P_j), where gcd is the greatest\ncommon divisor, and the maximization is over all pairs P_i, P_j \u2208 P.\nSufficiency is shown via a constructive proof, leading to a new\nperiod estimation algorithm.", "doi": "10.1109/ISCAS.2016.7527468", "isbn": "978-1-4799-5341-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-05", "pages": "1226-1229" }, { "id": "authors:yzyxm-7nz73", "collection": "authors", "collection_id": "yzyxm-7nz73", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160823-094540045", "type": "book_section", "title": "Coprime coarray interpolation for DOA estimation via nuclear norm minimization", "book_title": "2016 IEEE International Symposium on Circuits and Systems (ISCAS)", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" } ], "abstract": "Coprime arrays, consisting of two uniform linear arrays whose inter-element separations are coprime, can resolve O(MN) sources using only O(M + N) sensors. However, holes in the coarray prevent us from using the full coarray in the MUSIC algorithm for DOA estimation. Through interpolation, it may be possible to use the remaining elements of the coarray to increase the degrees of freedom beyond what is captured in the contiguous ULA section in the coarray. Techniques like positive definite Toeplitz completion, array interpolation, and sparse recovery, manage to include all the information in the coarray, but they demand extra fine-tuned parameters and have individual drawbacks. In this paper, a simple and tractable convex framework via nuclear norm minimization is presented. This approach has no extra tuning parameters and overcomes several undesired issues of other techniques. Numerical examples indicate that, in many instances, the proposed method not only increases the estimation accuracy but also distinguishes more sources than other methods.", "doi": "10.1109/ISCAS.2016.7539135", "isbn": "978-1-4799-5341-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-05", "pages": "2639-2642" }, { "id": "authors:mvff9-33333", "collection": "authors", "collection_id": "mvff9-33333", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160823-082935859", "type": "book_section", "title": "Detecting tandem repeats in DNA using Ramanujan Filter Bank", "book_title": "2016 IEEE International Symposium on Circuits and Systems (ISCAS)", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Tandem repeats are periodic segments in the DNA. They play an important role in forensics, tracing population evolution, genetic disorders and so on. Locating them in long DNA sequences is the problem addressed in this paper. A new technique is presented, based on the recently proposed Ramanujan Filter Bank (RFB). The RFB was shown to offer several advantages over the traditional period estimation techniques in DSP, such as those based on spectral estimation (STFT etc.). It involves simple integer operations, and detects several new repeats that could not be identified by popular existing techniques.1 Project Website: see [16].", "doi": "10.1109/ISCAS.2016.7527160", "isbn": "978-1-4799-5341-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-05", "pages": "21-24" }, { "id": "authors:yjsbe-gs842", "collection": "authors", "collection_id": "yjsbe-gs842", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160524-075304286", "type": "book_section", "title": "Graph filter banks with M-channels, maximal decimation, and perfect reconstruction", "book_title": "2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Signal processing on graphs finds applications in many areas. Motivated by recent developments, this paper studies the concept of spectrum folding (aliasing) for graph signals under the downsample-then-upsample operation. In this development, we use a special eigenvector structure that is unique to the adjacency matrix of M-block cyclic matrices. We then introduce M-channel maximally decimated filter banks. Manipulating the characteristics of the aliasing effect, we construct polynomial filter banks with perfect reconstruction property. Later we describe how we can remove the eigenvector condition by using a generalized decimator. In this study graphs are assumed to be general with a possibly non-symmetric and complex adjacency matrix.", "doi": "10.1109/ICASSP.2016.7472446", "isbn": "978-1-4799-9988-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-03", "pages": "4089-4093" }, { "id": "authors:ez1be-e4350", "collection": "authors", "collection_id": "ez1be-e4350", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160322-153051833", "type": "book_section", "title": "Super Nested Arrays: Sparse arrays with Less Mutual Coupling than Nested Arrays", "book_title": "2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). Sparse arrays, such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs), have reduced mutual coupling compared to uniform linear arrays (ULAs). With N denoting the number of sensors, these sparse arrays offer O(N^2) freedoms for source estimation because\ntheir difference coarrays have O(N^2)-long ULA segments. These arrays have different shortcomings: coprime arrays have holes in the coarray, MRAs have no closed-form expressions, and nested arrays have relatively large mutual coupling. This paper introduces a new array called the super nested array, which has all the good properties\nof the nested array, and at the same time reduces mutual coupling significantly. For fixed N, the super nested array has the same physical aperture, and the same hole-free coarray as does the nested array. But the number of sensor pairs with separation \u03bb/2 is significantly\nreduced. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays.", "doi": "10.1109/ICASSP.2016.7472223", "isbn": "978-1-4799-9988-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-03", "pages": "2976-2980" }, { "id": "authors:r817k-k7843", "collection": "authors", "collection_id": "r817k-k7843", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160901-122213310", "type": "book_section", "title": "Tensor MUSIC in Multidimensional Sparse Arrays", "book_title": "Signals, Systems and Computers, 2015", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Tensor-based MUSIC algorithms have been successfully applied to parameter estimation in array processing. In this paper, we apply these for sparse arrays, such as nested arrays and coprime arrays, which are known to boost the degrees of freedom to O(N2) given O(N) sensors. We consider two tensor decomposition methods: CANDECOMP/PARAFAC (CP) and high-order singular value decomposition (HOSVD) to derive novel tensor MUSIC spectra for sparse arrays. It will be demonstrated that the tensor MUSIC spectrum via HOSVD suffers from cross-term issues while the tensor MUSIC spectrum via CP identifies sources unambiguously, even in high- dimensional tensors.", "doi": "10.1109/ACSSC.2015.7421458", "isbn": "978-1-4673-8574-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2015-11", "pages": "1783-1787" }, { "id": "authors:nzah3-fz671", "collection": "authors", "collection_id": "nzah3-fz671", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160901-150342165", "type": "book_section", "title": "Minimal Dictionaries For Spanning Periodic Signals", "book_title": "Signals, Systems and Computers, 2015", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Recently, several high dimensional dictionary representations were proposed for discrete time periodic signals. These dictionaries could span any periodic signal whose period lies in a given range 1 \u2264 P \u2264 P_(max). Such dictionaries were used in various ways to estimate unknown periods. In this work, we derive some fundamental properties that any such dictionary must satisfy. For example, we derive bounds on the minimum size of such dictionaries, necessary conditions on their composition, and so on. Our results also demonstrate a natural connection between the well-known Euler Totient function (\u03c6-function) from number theory, and periodicity analysis.", "doi": "10.1109/ACSSC.2015.7421183", "isbn": "978-1-4673-8574-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2015-11", "pages": "523-527" }, { "id": "authors:0m20k-px956", "collection": "authors", "collection_id": "0m20k-px956", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160901-111008998", "type": "book_section", "title": "Fundamentals of multirate graph signal processing", "book_title": "Signals, Systems and Computers, 2015", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-O" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In this work, the fundamental blocks of multirate signal processing on graphs are analyzed. First the decimator is defined, and expander is solved accordingly. Then, noble identities and lazy filter bank for graph signals are constructed. After decimation, the length of the signal changes and the original adjacency matrix is not applicable. Therefore, such equations on graphs do not exist in general. For noble identities to exist and lazy filter bank to provide perfect reconstruction, the necessary and sufficient conditions on the graph are derived. Some graph examples, on which the conditions are satisfied, are also provided.", "doi": "10.1109/ACSSC.2015.7421460", "isbn": "978-1-4673-8574-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2015-11", "pages": "1791-1795" }, { "id": "authors:v04aq-02622", "collection": "authors", "collection_id": "v04aq-02622", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160901-151528946", "type": "book_section", "title": "Period Estimation and Tracking: Filter Bank Design Using Truth Tables of Logic", "book_title": "Signals, Systems and Computers, 2015", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Recently, a new filter-bank known as the Ramanujan Filter Bank (RFB) was proposed to detect, estimate and track periodic behavior in data, with several advantages over the traditional methods. Apart from period estimation, the RFB can determine if a given periodic signal is actually a sum of multiple periodic signals with smaller periods. But if one is only interested in period estimation, it is shown in this paper that filter- banks with far fewer filters than the RFB can be designed. These new designs use ideas from digital logic analysis to substantially reduce the number of filters in the RFB.", "doi": "10.1109/ACSSC.2015.7421410", "isbn": "978-1-4673-8574-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2015-11", "pages": "1566-1570" }, { "id": "authors:g5qgc-wtf51", "collection": "authors", "collection_id": "g5qgc-wtf51", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160105-083539088", "type": "book_section", "title": "Properties of Ramanujan filter banks", "book_title": "23rd European Signal Processing Conference (EUSIPCO)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tenneti", "given_name": "S.", "clpid": "Tenneti-S" } ], "abstract": "This paper studies a class of filter banks called the Ramanujan filter banks which are based on Ramanujan-sums. It is shown that these filter banks have some important mathematical properties which allow them to reveal localized hidden periodicities in real-time data. These are also compared with traditional comb filters which are sometimes used to identify periodicities. It is shown that non-adaptive comb filters cannot in general reveal periodic components in signals unless they are restricted to be Ramanujan filters. The paper also shows how Ramanujan filter banks can be used to generate time-period plane plots which track the presence of time varying, localized, periodic components.", "doi": "10.1109/EUSIPCO.2015.7362898", "isbn": "978-0-9928626-3-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2015-09", "pages": "2816-2820" }, { "id": "authors:2jeyx-thq78", "collection": "authors", "collection_id": "2jeyx-thq78", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160722-154315536", "type": "book_section", "title": "Ramanujan filter banks for estimation and tracking of periodicities", "book_title": "2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth V.", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We propose a new filter-bank structure for the estimation and tracking of periodicities in time series data. These filter-banks are inspired from recent techniques on period estimation using high-dimensional dictionary representations for periodic signals. Apart from inheriting the numerous advantages of the dictionary based techniques over conventional period-estimation methods such as those using the DFT, the filter-banks proposed here expand the domain of problems that can be addressed to a much richer set. For instance, we can now characterize the behavior of signals whose periodic nature changes with time. This includes signals that are periodic only for a short duration and signals such as chirps. For such signals, we use a time vs period plane analogous to the traditional time vs frequency plane. We will show that such filter banks have a fundamental connection to Ramanujan Sums and the Ramanujan Periodicity Transform.", "doi": "10.1109/ICASSP.2015.7178692", "isbn": "978-1-4673-6997-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2015-04", "pages": "3851-3855" }, { "id": "authors:pk4j7-gvv61", "collection": "authors", "collection_id": "pk4j7-gvv61", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160722-161857773", "type": "book_section", "title": "Multidimensional Ramanujan-sum expansions on nonseparable lattices", "book_title": "2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "It is well-known that the Ramanujan-sum c_q(n) has applications in the analysis of periodicity in sequences. Recently the author developed a new type of Ramanujan-sum representation especially suited for finite duration sequences x(n): This is based on decomposing x(n) into a sum of signals belonging to so-called Ramanujan subspaces S_(qi). This offers an efficient way to identify periodic components using integer computations and projections, since c_q(n) is integer valued. This paper revisits multidimensional signals with periodicity on possibly nonseparable integer lattices. Multidimensional Ramanujan-sum and Ramanujan-subspaces are developed for this case. A Ramanujan-sum based expansion for multidimensional signals is then proposed, which is useful to identify periodic components on nonseparable lattices.", "doi": "10.1109/ICASSP.2015.7178655", "isbn": "978-1-4673-6997-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2015-04", "pages": "3666-3670" }, { "id": "authors:17d5f-z1647", "collection": "authors", "collection_id": "17d5f-z1647", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160722-155946933", "type": "book_section", "title": "Coprime DFT filter bank design: Theoretical bounds and guarantees", "book_title": "2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Coprime DFT filter banks (coprime DFTFB) achieve the effect of an MN-DFTFB by using two DFTFBs of size only M and N, where M and N are coprime integers. However, coprime DFTFBs need to be designed properly, to avoid unwanted bumps in stopbands or unsatisfactory total spectrum coverage, quantified by overall amplitude responses. In this paper, a detailed theoretical analysis will be made on the tradeoffs between bumps and overall amplitude responses. It will be shown that the bump level at the center frequency f_b of a bump, is approximately one-fourth of the overall amplitude response at f_b. Then, a novel design will be introduced based on an optimization problem pertaining to overall amplitude responses. The original problem is relaxed to a computationally tractable optimization program, which can be solved with alternating minimization algorithms. It is verified with simulations that the new designs cover the spectrum completely.", "doi": "10.1109/ICASSP.2015.7178694", "isbn": "978-1-4673-6997-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2015-04", "pages": "3861-3865" }, { "id": "authors:jqrjm-fzx30", "collection": "authors", "collection_id": "jqrjm-fzx30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160722-143825916", "type": "book_section", "title": "Coprime arrays and samplers for space-time adaptive processing", "book_title": "2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper extends the use of coprime arrays and samplers for the case of moving sources. Space-time adaptive processing (STAP) plays an important role in estimating direction-of-arrivals (DOAs) and radial velocities of emitting sources. However, the detection performance is fundamentally limited by the array geometry and the temporal samplers at each sensor. Coprime arrays and coprime samplers offer an enhanced degree of freedom of O(MN) using only O(M + N) physical sensors or samples. In this paper, we propose coprime joint angle-Doppler estimation (coprime JADE), which incorporates both coprime arrays and coprime samplers with the STAP framework. Nonuniform time samples at different sensors can be used to generate a sampled autocorrelation matrix, from which we compute a spatial smoothed matrix. It will be proved that spatial smoothed matrices can be used in the MUSIC algorithm for parameter estimation. With sufficient snapshots, coprime JADE distinguishes O(M_1N_1M_2N_2) independent sources if it corresponds to coprime arrays and coprime samplers with coprime integers (M_1,N_1) and (M_2,N_2), respectively. It is verified through simulations that coprime JADE resolves the angle-Doppler information better compared to other conventional algorithms.", "doi": "10.1109/ICASSP.2015.7178394", "isbn": "978-1-4673-6997-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2015-04", "pages": "2364-2368" }, { "id": "authors:dtk77-c9361", "collection": "authors", "collection_id": "dtk77-c9361", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150508-140006588", "type": "book_section", "title": "Gridless methods for underdetermined source estimation", "book_title": "48th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The performances of two gridless algorithms for direction of arrival estimation are analyzed, when the number of sources can be larger than the number of array elements. One of these algorithms is a hybrid scheme recently proposed by the authors that uses low rank recovery techniques, and the other is based on total variation (TV) norm minimization scheme. It is shown that when a nested sensor array is used, and the source signals are assumed to be Gaussian, these recovery algorithms can recover O(M^2) sources using M sensors with overwhelming probability in the number of time snapshots.", "doi": "10.1109/ACSSC.2014.7094408", "isbn": "978-1-4799-8295-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2014-11", "pages": "111-115" }, { "id": "authors:09x3e-ak131", "collection": "authors", "collection_id": "09x3e-ak131", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150508-143118886", "type": "book_section", "title": "Dictionary approaches for identifying periodicities in data", "book_title": "48th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We propose several dictionary representations for periodic signals and use them for estimating their periodicity. This includes estimating concurrent multiple periodicities. These are inspired from the recently proposed DFT based Farey dictionary, where period estimation was cast as a sparse vector recovery problem. We show that this can instead be framed as an l2 norm based data-fitting problem with closed form solutions and much faster computations. We also generalize the complex valued Farey dictionary to simpler integer valued dictionaries. We find that dictionaries constructed using the recently proposed Ramanujan Periodicity Transforms provide the best trade-off between complexity and noise immunity.", "doi": "10.1109/ACSSC.2014.7094814", "isbn": "978-1-4799-8295-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2014-11", "pages": "1967-1971" }, { "id": "authors:87hj8-z1q27", "collection": "authors", "collection_id": "87hj8-z1q27", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150508-123246910", "type": "book_section", "title": "Design of coprime DFT arrays and filter banks", "book_title": "48th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Coprime arrays offer degrees of freedom of O(MN) given O(M +N) sensors, where M and N are coprime integers. The performance of coprime arrays is based on coprime DFT filter banks (coprime DFTFBs), which cascade an M-channel DFTFB and an N-channel DFTFB to achieve MN-channel filter banks. However, practical designs of coprime DFTFBs have not been fully studied. In this paper, a systematic design is related to IFIR filter designs, based on M, N, filter orders, and peak ripples. Our design owns a parameter \u03bb that provides tradeoffs between passbands and stopbands. A design example for different \u03bb is also presented.", "doi": "10.1109/ACSSC.2014.7094484", "isbn": "978-1-4799-8295-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2014-11", "pages": "455-459" }, { "id": "authors:wq0et-p5412", "collection": "authors", "collection_id": "wq0et-p5412", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150508-141226938", "type": "book_section", "title": "Ramanujan subspaces and digital signal processing", "book_title": "48th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tenneti", "given_name": "Srikanth", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" } ], "abstract": "Ramanujan-sums have in the past been used to extract hidden periods. In a recent paper it was shown that for finite duration (FIR) sequences, the traditional representation is not suitable. Two new types of Ramanujan-sum expansions were proposed for the FIR case, each offering an integer basis, and applications in the extraction of hidden periodicities were developed. Crucial to these developments was the introduction of Ramanujan spaces. The aim of this paper is to develop some properties of these subspaces in the context of signal processing. The design of near orthogonal bases for these spaces is emphasized.", "doi": "10.1109/ACSSC.2014.7094770", "isbn": "978-1-4799-8295-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2014-11", "pages": "1762-1766" }, { "id": "authors:30tr8-ze389", "collection": "authors", "collection_id": "30tr8-ze389", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150922-131543497", "type": "book_section", "title": "Soft-thresholding for spectrum sensing with coprime samplers", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Coprime Sampling has been recently proposed to efficiently estimate the spectrum of wideband signals, using sampling rates which can be significantly lower than the Nyquist rate. While the method has been shown to work well when large number of samples are available for estimating the autocorrelation, the effect of fewer samples on the performance of coprime spectrum estimation has not been addressed so far. This paper addresses this issue by employing a denoising scheme on the spectral estimates, as a l_1 norm penalized quadratic program. The solution to this problem results in the so-called soft thresholding operator on the spectral estimates, which inherently promotes sparsity. It also helps to combat the effect of spurious peaks resulting from the finite sample averaging. The probabilities of detecting active and inactive bands are also explicitly characterized and they converge to unity by increasing the number (L) of sub Nyquist samples available to compute the estimates. The effectiveness of the proposed method is demonstrated through numerical examples.", "doi": "10.1109/SAM.2014.6882456", "publisher": "IEEE", "publication_date": "2014-06" }, { "id": "authors:k3xw5-byr96", "collection": "authors", "collection_id": "k3xw5-byr96", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150106-133053650", "type": "book_section", "title": "Ramanujan-sum expansions for finite duration (FIR) sequences", "book_title": "2014 IEEE International Conference on Acoustics, Speech and Signal Processing", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Ramanujan sums have in the past been used to represent arithmetic sequences. It is shown here that for finite duration (FIR) sequences with length N, the traditional representation is not suitable. Two new types of Ramanujan-sum expansions are proposed here for the FIR case, each offering an integer basis. One of these is particularly suited to identify periodicities in the FIR sequence. This representation in fact expresses any FIR sequence as a sum of orthogonal sequences each with a hidden periodicity corresponding to a divisor of N.", "doi": "10.1109/ICASSP.2014.6854540", "isbn": "978-1-4799-2892-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2014-05", "pages": "4933-4937" }, { "id": "authors:wy5y4-dja05", "collection": "authors", "collection_id": "wy5y4-dja05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150106-131405050", "type": "book_section", "title": "Parameter identifiability in Sparse Bayesian Learning", "book_title": "2014 IEEE International Conference on Acoustics, Speech and Signal Processing", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The problem of parameter identifiability in linear underdetermined models is addressed, where the observed data vectors follow a multivariate Gaussian distribution. The problem is underdetermined because the dimension of parameters characterizing the distribution of the data is larger than the dimension of the observed vectors. Such models arise frequently in Bayesian Compressive sensing and Sparse Bayesian Learning problems, where the parameter vector to be estimated, is assumed to be sparse. We establish explicit conditions for parameter identifiability in such models, by relating the ambient dimension of the hyperparameter space and that of the data. We establish a crucial result that in such underdetermined models, even without requiring the parameter to be sparse, it is possible to guarantee unique identifiability of the parameters as long as these two dimensions satisfy a certain condition. When such a condition is violated, the unconstrained statistical model is no more identifiable and additional constraints in the form of sparsity need to be enforced to recover the true parameter.", "doi": "10.1109/ICASSP.2014.6853919", "isbn": "978-1-4799-2892-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2014-05", "pages": "1851-1855" }, { "id": "authors:hyng9-q0q38", "collection": "authors", "collection_id": "hyng9-q0q38", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150106-130755371", "type": "book_section", "title": "The Farey-dictionary for sparse representation of periodic signals", "book_title": "2014 IEEE International Conference on Acoustics, Speech and Signal Processing", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" } ], "abstract": "A finite duration sequence exhibiting periodicities does not in general admit a sparse representation in terms of the DFT basis unless the period is a divisor of the duration. This paper develops a dictionary called the Farey dictionary for the efficient representation of such sequences. It is shown herein that this representation is especially useful for identifying hidden periodicities in a finite data record. The properties of the Farey dictionary are studied, and the dictionary is shown to be superior to the conventional DFT based uniform dictionary, from the view point of identifying hidden periods.", "doi": "10.1109/ICASSP.2014.6853618", "isbn": "978-1-4799-2892-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2014-05", "pages": "360-364" }, { "id": "authors:v5zay-np098", "collection": "authors", "collection_id": "v5zay-np098", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141020-071754311", "type": "book_section", "title": "Reflections on Sampling-Filters for Compressive Sensing and Finite-Innovations-Rate Models", "book_title": "47th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tenneti", "given_name": "Srikanth", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-S-V" } ], "contributor": [ { "family_name": "Matthews", "given_name": "Michael B.", "clpid": "Matthews-M-B" } ], "abstract": "This paper revisits sampling-filters for signals having\na finite rate of innovations. Such filters arise in many applications including digital communications and compressive sensing, and mulitchannel versions of these systems have been considered in the past. The main focus of this paper is on sampling-filters that result in perfect reconstruction (PR), or zero-forcing (ZF). Conditions for existence of these filters are expressed both in terms of bandwidth requirement and in the framework of Riesz basis. Many practical advantages induced by the Riesz basis property are also pointed out. When the sampling filters for\nPR exist, they are in general not unique. Optimum filters that minimize the effect of noise are discussed and compared with energy compaction filters, which are suboptimal.", "doi": "10.1109/ACSSC.2013.6810584", "isbn": "978-1-4799-2388-5", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2013-11", "pages": "1672-1676" }, { "id": "authors:f2ate-z7v12", "collection": "authors", "collection_id": "f2ate-z7v12", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141021-071826078", "type": "book_section", "title": "Conditions for Identifiability in Sparse Spatial Spectrum Sensing", "book_title": "21st European Signal Processing Conference (EUSIPCO)", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Spatial Spectrum estimation is a key technique used in a wide variety of problems arising in signal processing and communication, particularly those employing multiple antennas. In many scenarios such as direction finding using antenna arrays, it is crucial to estimate which directions in space contribute to active sources (indicated by a non zero power). It has been recently shown that if the sources from different directions are statistically uncorrelated, it is possible to identify as many as O(M2) active sources using only M physical antennas. A sparse representation for the spatial spectrum was further exploited to reconstruct the spectrum using convex optimization techniques. In this paper, we consider the situation when there is non zero cross correlation between the sources impinging from different directions. We investigate if, fundamentally, it still possible to identify more sources than the number of physical sensors and what role the cross correlation terms play. Recovery guarantees are developed to ensure uniqueness of the sparse representation for spectrum sensing. They are further extended to establish conditions under which a greedy heuristic, namely the Orthogonal Matching Pursuit algorithm will successfully recover the sparse spectrum. It is shown that in both cases, it is possible to recover support of larger size provided the correlation terms are small compared to the power of the impinging signals.", "isbn": "9781479936878", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2013-09", "pages": "1832-1836" }, { "id": "authors:5r6vq-rbj83", "collection": "authors", "collection_id": "5r6vq-rbj83", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170130-170601430", "type": "book_section", "title": "Analog filter banks for sampling: Discretization, polyphase form, and role in compressive sensing", "book_title": "2013 IEEE Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Continuous-time signals arising in many applications can often be modeled as the outputs of analog synthesis-filter banks driven by discrete-time inputs d_i(n). Such a signal x(t) has a finite innovations rate, although it may not be bandlimited in general. In some applications it is necessary to sample such signals after filtering with an analog sampling-filter-bank, to recover the driving signals di(n): This sampling filter bank is in general not unique, and the theory and design techniques for such analog filter banks are not as well developed as the large body of literature on digital filter banks. In this paper we show that the theoretical as well as design and implementation issues can be formulated in terms of digital filter banks, by taking advantage of the finite innovations rate of x(t): The rich body of knowledge on digital filter banks and polyphase forms can therefore be utilized and furthermore the optimization of the sampling filter bank can be done on a more convenient platform. Applications of this development in the context of compressive sensing are also elaborated.", "doi": "10.1109/DSP-SPE.2013.6642559", "isbn": "978-1-4799-1616-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2013-08", "pages": "24-29" }, { "id": "authors:fk757-1qk10", "collection": "authors", "collection_id": "fk757-1qk10", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140225-110454867", "type": "book_section", "title": "Correlation-aware sparse support recovery: Gaussian sources", "book_title": "2013 IEEE International Conference on Acoustics, Speech, and Signal Processing", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Consider a multiple measurement vector (MMV) model given by y[n] = Ax_s[n]; 1 \u2264 n \u2264 L where {y[n]}^L_n=1 denote the L measurement vectors, A \u2208 R^(M\u00d7N) is the measurement matrix and x_s[n] \u2208 R^N are the unknown vectors with same sparsity support denoted by the set S_0 with |S_0| = D. It has been shown in a recent paper by the authors that when the elements of x_s[n] are uncorrelated from each other, one can recover sparsity levels as high as O(M^2) for suitably designed measurement matrix. The recovery is exact when support recovery algorithms are applied on the ideal correlation matrix. When we only have estimates of the correlation, it is still possible to probabilistically argue the recovery of sparsity levels (using a coherence based argument) that is much higher than that guaranteed by existing coherence based results. However the lower bound on the probability of success is found to increase rather slowly with L (as 1-C/L for some constant C > 0) without any further assumption on the distribution of the source vectors. In this paper, we demonstrate that when the source vectors belong to a Gaussian distribution with diagonal covariance matrix, it is possible to guarantee the recovery of original support with overwhelming probability. We also provide numerical simulations to demonstrate the effectiveness of the proposed strategy by comparing it with other popular MMV based methods.", "doi": "10.1109/ICASSP.2013.6638792", "isbn": "978-1-4799-0356-6", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2013-05", "pages": "5880-5884" }, { "id": "authors:nnx3p-qnf53", "collection": "authors", "collection_id": "nnx3p-qnf53", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170705-171129924", "type": "book_section", "title": "Coprime Sampling and Arrays in One and Multiple Dimensions", "book_title": "Multiscale Signal Analysis and Modeling", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" } ], "contributor": [ { "family_name": "Shen", "given_name": "Xiaoping", "clpid": "Shen-Xiaoping" }, { "family_name": "Zayed", "given_name": "Ahmed I.", "clpid": "Zayed-A-I" } ], "abstract": "his chapter gives an overview of the concept of coprime sampling. The basic idea is that a continuous-time (or spatial) signal is sampled simultaneously by two sets of samplers, with sampling rates 1\u2215MT and 1\u2215NT where M and N are coprime integers and T>0. One of the results is that it is possible to estimate the autocorrelation of the signal at a much higher rate (=1/T) than the total sampling rate. Thus, any application which is based on autocorrelation will benefit from such sampling and reconstruction. One example is in array processing, in the context of estimation of direction of arrival (DOA) of sources. Traditionally, an array with L sensors would be able to identify L \u2212 1 independent sources, but with a pair of coprime arrays, one can identify O(L2) sources. It is also shown how to use two DFT filter banks, one in conjunction with each sampling array, to produce a much denser tiling of the frequency domain than each filter bank would individually be able to do. This chapter also discusses the extension of coprime sampling to multiple dimensions by using sampling geometries that are defined based on lattices. In this context the generation of coprime pairs of integer matrices is a very interesting mathematical problem and is dealt with in detail. The use of coprime samplers in system identification is also elaborated upon. A brief review of fractionally spaced equalizers in digital communications, in the context of coprime sampling, is included.", "doi": "10.1007/978-1-4614-4145-8_5", "isbn": "978-1-4614-4144-1", "publisher": "Springer", "place_of_publication": "New York, NY", "publication_date": "2013", "pages": "105-137" }, { "id": "authors:rh0dj-cwp97", "collection": "authors", "collection_id": "rh0dj-cwp97", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141020-080154070", "type": "book_section", "title": "Why does direct-MUSIC on sparse-arrays work?", "book_title": "47th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" } ], "abstract": "The nested and coprime arrays have recently been introduced as systematic structures to construct difference coar-rays with O(m^2) elements, where m is the number of array elements. They are therefore able to identify O(m^2) sources (or DOAs) under the assumption that the sources are uncorrelated. In view of their larger aperture compared to uniform linear arrays (ULAs) with the same number of elements, these arrays have some advantages over conventional ULAs even in the cases where the number of sources is less than m, such as improved Cramer-Rao bounds and improved resolvability for closely spaced sources. It has recently been shown that in such situations and under mild assumptions on source locations, it is possible to use subspace techniques such as the MUSIC algorithm directly on these sparse arrays, instead of on the coarrays, thereby making the resulting algorithms simpler. Thus the ambiguity introduced by the sparsity of the arrays is overcome with the help of extra elements with coprime spacing, even if there are multiple sources. The purpose of this paper is to give the theoretical justification for this.", "doi": "10.1109/ACSSC.2013.6810658", "isbn": "978-1-4799-2388-5", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2013", "pages": "2007-2011" }, { "id": "authors:pypw3-qcp72", "collection": "authors", "collection_id": "pypw3-qcp72", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130802-080004882", "type": "book_section", "title": "Role of bandwidth in the quality of inversion of linear multirate systems with noise", "book_title": "Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" } ], "abstract": "A multirate system called the fractional sampling rate alteration system makes frequent appearance in many signal processing applications including fractionally spaced equalizers (FSE) and in multirate feedback control. In some applications it is necessary to invert this system, as in the example of a zero-forcing FSE. There is usually noise at the input of the inverse, and the noise amplification properties depend crucially on the bandwidth of the original system, as shown in this paper. Even though this effect is qualitatively known in FSE applications, the purpose of this paper is to provide the quantitative theoretical foundations for this effect. It will be shown that if the system has excess bandwidth, then the noise gain can be readily controlled, whereas unbounded noise amplification can result if there is no excess bandwidth.", "doi": "10.1109/ACSSC.2012.6489219", "isbn": "978-1-4673-5050-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2012-11", "pages": "1233-1237" }, { "id": "authors:39254-3wg05", "collection": "authors", "collection_id": "39254-3wg05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130802-073220147", "type": "book_section", "title": "Max-rate MIMO broadcast DFE transceiver design under power and SER constraints", "book_title": "2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)", "author": [ { "family_name": "Liu", "given_name": "Chih-Hao", "clpid": "Liu-Chih-Hao" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper studies the joint design problem of a decision feedback equalizer (DFE) transceiver and bit allocation for multi-input multi-output (MIMO) broadcast channels. The design problem is formulated as a transmission rate maximization problem for given power and symbol error rate (SER) specifications. The optimal bit allocation is derived. Under some conditions, to be described later, there exists a particular class of joint triangularization (JT) which can be applied to obtain the optimal broadcast DFE transceiver for the max-rate problem with quality of service (QoS) constraints. The optimal joint design is called the maximum rate JT broadcast DFE transceiver (MRJT). A suboptimal design, the rate maximized QR broadcast DFE transceiver (RMQR), which is always possible, is also proposed. In the simulations, several numerical results are given to demonstrate the bit rate performance of the proposed MRJT and RMQR broadcast DFE transceivers under different QoS specifications.", "doi": "10.1109/ACSSC.2012.6489053", "isbn": "978-1-4673-5050-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2012-11", "pages": "494-498" }, { "id": "authors:ydbmy-06c30", "collection": "authors", "collection_id": "ydbmy-06c30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130806-102757073", "type": "book_section", "title": "On Application of LASSO for Sparse Support Recovery With Imperfect Correlation Awareness", "book_title": "2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Matthews", "given_name": "M. B.", "clpid": "Matthews-M-B" } ], "abstract": "In this paper, the problem of identifying the common sparsity support of multiple measurement vectors (MMV) is considered. The model is given by y[n] = Ax_s[n], 1 \u2264 n \u2264 L where {y[n]}^(L)n=1 denote the L measurement vectors, A \u2208 R^(M\u00d7N) is the measurement matrix and x_s[n] \u2208 R^N are the unknown vectors with same sparsity support denoted by the set S_0 with |S_0| = D. It has been shown in a recent paper by the authors that when the elements of x_s[n] are uncorrelated from each other, one can recover sparsity levels as high as O(M^2) for suitably designed measurement matrix. This result was shown assuming the knowledge that the nonzero elements are perfectly uncorrelated and that we have perfect estimates for the data correlation matrix, (the latter is true in the limit as L \u2192 \u221e). In this paper, we formulate the problem of support recovery in the non ideal setting, i.e., when the correlation matrix is estimated with finite L. The resulting support recovery problem which explicitly utilizes the correlation knowledge, can be formulated as a LASSO. The performance of such \"correlation aware\" LASSO is analyzed by providing lower bounds on the probability of successful recovery as a function of the number L of measurement vectors. Numerical results are also provided to demonstrate the superior performance of the proposed correlation aware framework over conventional MMV techniques under identical conditions.", "doi": "10.1109/ACSSC.2012.6489158", "isbn": "978-1-4673-5050-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2012-11", "pages": "958-962" }, { "id": "authors:jw948-2n941", "collection": "authors", "collection_id": "jw948-2n941", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130802-074219937", "type": "book_section", "title": "Compressive sensing and filter-bank signal models", "book_title": "2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "A compressible signal can often be modeled as a sum of outputs of subband filters of a synthesis filter bank. This model allows one to find compressive sampling schemes, whereby the original continuous signal can directly be acquired by sampling at a very low (sub-Nyquist) rate. This paper revisits this result from the view point of filter bank theory. This is motivated by recent work by Mishali and Eldar on the so-called Xampling techniques for compressible signals. The viewpoint presented here emphasizes the simplicity and directness of the compressive sensing idea and also places in evidence the framework which can be used to formulate optimal compressive sampling problems.", "doi": "10.1109/ACSSC.2012.6489078", "isbn": "978-1-4673-5050-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2012-11", "pages": "603-607" }, { "id": "authors:6kvzd-d9s41", "collection": "authors", "collection_id": "6kvzd-d9s41", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121011-130930015", "type": "book_section", "title": "MIMO broadcast DFE transceiver design with bit allocation under QoS constraints", "book_title": "2012 IEEE Statistical Signal Processing Workshop", "author": [ { "family_name": "Liu", "given_name": "Chih-Hao", "clpid": "Liu-Chih-Hao" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper considers the joint design problem of linear precoder, decision feedback equalizer (DFE) and bit allocation for multi-input multi-output (MIMO) broadcast (BC) channels. The problem is formulated as the power minimization problem when the target bit rate and per stream symbol error rate (SER) are specified. For the two-user case, a particular class of joint triangularization (JT) can be applied to obtain the optimal design for the joint optimization problem with quality of service (QoS) constraints, namely, the Minimum Power JT broadcast DFE transceiver (MPJT). For arbitrary number of users, a suboptimal design, the Power Minimized QR DFE broadcast transceiver (PMQR), is also proposed. Numerical results are presented to demonstrate the performance of MPJT and PMQR transceivers under different QoS constraints.", "doi": "10.1109/SSP.2012.6319739", "isbn": "978-1-4673-0182-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2012-10-11", "pages": "488-491" }, { "id": "authors:4pxe8-3zz89", "collection": "authors", "collection_id": "4pxe8-3zz89", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121011-143607324", "type": "book_section", "title": "Correlation-aware techniques for sparse support recovery", "book_title": "2012 IEEE Statistical Signal Processing Workshop", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Sparse support recovery techniques guarantee successful recovery of sparse solutions to linear underdetermined systems provided the measurement matrix satisfies certain conditions. The maximum level of sparsity that can be recovered with existing algorithms is O(M) where M denotes the size of the measurement vector. This paper shows how this can be improved to O(M^2) by assuming certain prior knowledge about the correlation structure of the measurements. The theory for correlation aware framework for support recovery is developed, which involves the Khatri-Rao (KR) product of the measurement matrix. Necessary and sufficient conditions for unique recovery of the sparse support are provided for this new framework which outperforms the more traditional CS techniques in terms of required size of the measurement vector. It also gives rise to interesting questions of constructing classes of measurement matrices which can exploit the prior correlation knowledge in an effective way.", "doi": "10.1109/SSP.2012.6319753", "isbn": "978-1-4673-0182-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2012-10-11", "pages": "53-56" }, { "id": "authors:f99c2-xzw38", "collection": "authors", "collection_id": "f99c2-xzw38", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120907-100742710", "type": "book_section", "title": "Direct-MUSIC on sparse arrays", "book_title": "2012 International Conference on Signal Processing and Communications", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" } ], "abstract": "Nested and coprime arrays are sparse arrays which can identify O(m^2) sources using only m sensors. Systematic algorithms have recently been developed for such identification. These algorithms are traditionally implemented by performing MUSIC or a similar algorithm in the difference-coarray domain. This paper considers the use of nested and coprime arrays for the case where the number of sources is less than m. It will be demonstrated that there are some important advantages even in this case. With the number of sources limited like this, it is possible to use MUSIC directly on the nested or coprime array rather than in the coarray domain. But owing to array sparsity, the unambiguous identifiability property has to be revisited. This paper first mentions two results for such identifiability. Second, the improvement in the Cramer-Rao bound (over uniform linear arrays or ULAs) is analyzed. One conclusion is that the CRB improvements of nested and coprime arrays are comparable to those of other known sparse arrays such as MRAs. It is also observed that nested and coprime arrays have higher resolvability than the ULA, for a fixed number of sensors.", "doi": "10.1109/SPCOM.2012.6289992", "isbn": "978-1-4673-2013-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2012-07", "pages": "1-5" }, { "id": "authors:pfaeh-d4f52", "collection": "authors", "collection_id": "pfaeh-d4f52", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130225-104828989", "type": "book_section", "title": "Joint MAX-SER-Minimized DFE Transceiver Design with Bit Allocation for Broadcast Channels", "book_title": "2012 International Conference on Communications (ICC)", "author": [ { "family_name": "Liu", "given_name": "Chih-Hao", "clpid": "Liu-Chih-Hao" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper addresses the joint design problem of bit allocation and decision feedback equalizer (DFE) transceiver for multi-input multi-output (MIMO) broadcast (BC) channels. Channel state information (CSI) is assumed to be available both at the transmitter and receivers. The transceiver is designed by minimizing maximum symbol error rate (MAX-SER) under the total power and bitrate constraints. The bit allocation, precoder, feed-forward matrices and feedback matrices are the optimization variables. For the two-user case, a particular class of joint triangularization (JT) can be applied to obtain the optimal design for the problem, which is the optimal JT minimum Max-SER BC DFE transceiver (JTMMS). For arbitrary number of users, the suboptimal design, the QR BC DFE transceiver with bit allocation, is discussed. In the simulations, the Max-SER and average BER performance of the proposed systems are investigated.", "doi": "10.1109/ICC.2012.6364033", "isbn": "978-1-4577-2052-9", "publisher": "IEEE", "place_of_publication": "New York, NY", "publication_date": "2012-06", "pages": "3606-3610" }, { "id": "authors:4fmzp-rky95", "collection": "authors", "collection_id": "4fmzp-rky95", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170215-170654599", "type": "book_section", "title": "Low complexity generalized geometric mean decomposition and DFE transceiver design", "book_title": "2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Liu", "given_name": "Chih-Hao", "clpid": "Liu-Chih-Hao" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The complexity of the generalized geometric mean decomposition (GGMD) depends on the GGMD parameters. This paper consider the low complexity GGMD (LCGGMD) which has the least complexity within the class of GGMD. LCGGMD can be used in designing an optimal decision feedback equalizer (DFE) transceiver for a multi-input-multi-output (MIMO) channel. A novel iterative receiver detection algorithm for the receiver is also proposed. A LCGGMD transceiver always has less or equal design and implementation complexity as compared to a GMD DFE minimum mean square error (MMSE) transceiver. For the applications in which the SVDs of the equivalent MIMO channel matrices can be easily computed, such as cyclic prefix (CP) systems, the proposed LCGGMD transceiver has the most complexity-advantage over the GMD transceiver when the size of data block is highly factorable. In the simulations, LCGGMD transceivers are designed for CP systems and performance comparisons are made with well-known transceivers.", "doi": "10.1109/ACSSC.2011.6190284", "isbn": "978-1-4673-0323-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2011-11", "pages": "1574-1578" }, { "id": "authors:xdpz6-0yt06", "collection": "authors", "collection_id": "xdpz6-0yt06", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170307-172506688", "type": "book_section", "title": "Non uniform linear arrays for improved identifiability in cumulant based DOA Estimation", "book_title": "2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Direction of arrival (DOA) estimation methods based on arbitrary even order (2q, q \u2265 2) cumulants of the received data are known to be capable of identifying many more non Gaussian sources (O(N^q)) than the physical number (N) of sensors. However, in this paper, it is shown that the identifiability of 2qth order cumulant based DOA estimation can be significantly higher than this. This is due to the fundamental connection of the 2qth order cumulants with the concept of a 2qth order difference co-array, which is a virtual array determined solely by the physical array geometry. Depending on the sensor orientations, the 2qth order difference co-array can contain as many as O(N^(2q)) elements. In order to find a class of linear physical arrays which achieves this, a new generic class of non uniform linear arrays, namely the 2qth order nested array, is proposed, whose 2qth order difference co-array is proved to contain an uniform linear array (ULA) segment with O(N^(2q)) sensors. Also, to exploit these increased degrees of freedom of the co-array, a new algorithm for DOA estimation is developed, which starts from the same 2qth order cumulant matrix as the earlier methods and can yet identify O(N^(2q)) sources.", "doi": "10.1109/ACSSC.2011.6190074", "isbn": "978-1-4673-0323-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2011-11", "pages": "608-612" }, { "id": "authors:v3v7t-kcp67", "collection": "authors", "collection_id": "v3v7t-kcp67", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170214-170904544", "type": "book_section", "title": "Nonuniform sparse array design for active sensing", "book_title": "2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-Ching-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Active sensing using multiple transmitting elements and independent waveforms has recently attracted much attention. Using M transmitting and N receiving elements, one can virtually simulate a physical array of MN elements by the sum co-array. Nonuniform sparse arrays can further be used in active sensing to produce the difference co-array of the given sum co-array with dramatically increased degree of freedom. However, current literature lacks an efficient design method for active sensing with nonuniform sparse arrays. In this paper, we address this problem and propose several systematic construction methods based on some classical results in number theory. By using these methods, we are able to construct active sensing sparse arrays, in which the difference co-array of the sum-co-array has aperture in the order of O(M^2N^2). Furthermore, it has no holes within this aperture. Several performance bounds on the maximum aperture of the sparse array are then provided. These can be used in the future to compare the performance of other suboptimal nonuniform sparse array geometries.", "doi": "10.1109/ACSSC.2011.6190175", "isbn": "978-1-4673-0323-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2011-11", "pages": "1062-1066" }, { "id": "authors:rrd6a-hx858", "collection": "authors", "collection_id": "rrd6a-hx858", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170307-171741036", "type": "book_section", "title": "Two dimensional nested arrays on lattices", "book_title": "2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In this paper, we develop the theory of a new class of two dimensional arrays with sensors on lattice(s) which can be used to construct a virtual array of much larger size through passive processing. This structure is obtained by systematically nesting two arrays, one with sensors suitably placed on a sparse lattice and the other on an appropriately chosen dense lattice. The difference co-array of such an array with M and N elements respectively on the two lattices, is proved to be a larger two dimensional array with O(MN) sensors present contiguously (without holes) on the dense lattice. It will be shown that there is complete freedom to choose the sparse and dense arrays as long as they are related by an integer matrix (which can also be arbitrarily chosen). To exploit the increased degrees of freedom offered by the array for two dimensional DOA estimation of more sources than sensors, a novel algorithm based on the concept of two dimensional spatial smoothing is also proposed. The validity of the proposed methods is verified through numerical examples.", "doi": "10.1109/ICASSP.2011.5947004", "isbn": "978-1-4577-0539-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2011-05", "pages": "2548-2551" }, { "id": "authors:mfedv-59f26", "collection": "authors", "collection_id": "mfedv-59f26", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170215-171013633", "type": "book_section", "title": "Generalized geometric mean decomposition and DFE MMSE transceiver design for cyclic prefix systems", "book_title": "2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Liu", "given_name": "Chih-Hao", "clpid": "Liu-Chih-Hao" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper considers the decomposition of a complex matrix as the product of several sets of semi-unitary matrices and upper triangular matrices in iterative manner. The innermost triangular matrix has its diagonal elements equal to the geometric mean of the singular values of the complex matrix. This decomposition, generalized geometric mean decomposition (GGMD), has one order less complexity than the geometric mean decomposition (GMD) if the target matrix is a diagonal matrix. GGMD can be used to design the optimal decision feedback equalizer (DFE) MMSE transceiver for arbitrary multi-input-multi-output (MIMO) channels. The GGMD transceiver shares the same performance as the transceiver designed by using GMD. For the applications over cyclic prefix system, the GGMD transceiver has K/ log2(K) times lower complexity1 than the GMD transceiver, where K is the number of subchannels and is a power of 2.", "doi": "10.1109/ICASSP.2011.5947114", "isbn": "978-1-4577-0539-7", "publisher": "IEEE", "place_of_publication": "Piescataway, NJ", "publication_date": "2011-05", "pages": "3396-3399" }, { "id": "authors:pxech-6vw38", "collection": "authors", "collection_id": "pxech-6vw38", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170214-171534666", "type": "book_section", "title": "The role of GTD in optimizing biorthogonal filter banks", "book_title": "2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-Ching-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Filter bank optimization for specific input statistics has been of great interest in both theory and practice in many signal processing applications. In this paper we consider biorthogonal GTD (generalized triangular decomposition) filter banks for optimizing the coding gain. We develop some theoretical results for the optimal biorthogonal GTD subband coder. We also show in both theory and numerical simulations that biorthogonal GTD subband coders have superior performance than biorthogonal subband coders, orthonormal GTD subband coders, and orthonormal subband coders. In addition, the uniform bit loading scheme can with no loss of optimality be used in the optimal biorthogonal GTD coders, which does not have the granularity problem arising in the conventional optimum bit loading formula.", "doi": "10.1109/ICASSP.2011.5947322", "isbn": "978-1-4577-0539-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2011-05", "pages": "4372-4375" }, { "id": "authors:nk1km-7h574", "collection": "authors", "collection_id": "nk1km-7h574", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170307-171108058", "type": "book_section", "title": "Adjugate pairs of sparse arrays for sampling two dimensional signals", "book_title": "2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" } ], "abstract": "Sparse sampling with coprime lattice arrays was introduced recently in the literature. It has been shown that a dense coarray can be constructed from such a pair of arrays, and is useful in array processing and image processing applications. For example, the coarray allows one to identify many more sources than sensors. After a brief review of these fundamentals, this paper examines the case where the two arrays are generated by matrices that are adjugates of each other. In this case it is possible to obtain a dense rectangular tiling of the 2D frequency plane from a pair of coarse 2D DFT filter banks. The special case where the adjugate pairs are generated by skew circulant matrices has some advantages, which are examined in detail.", "doi": "10.1109/ICASSP.2011.5947213", "isbn": "978-1-4577-0539-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2011-05", "pages": "3936-3939" }, { "id": "authors:tjkr4-bej63", "collection": "authors", "collection_id": "tjkr4-bej63", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120416-081909814", "type": "book_section", "title": "Sparse coprime sensing with multidimensional lattice arrays", "book_title": "2011 IEEE Digital Signal Processing Workshop/IEEE Signal Processing Education Workshop (DSP/SPE)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" } ], "abstract": "Consider two uniform samplers operating simultaneously on a signal, with sample spacings MT and NT where M and N are coprime integers, and T has time or space dimension. It can be shown that the difference coarray of this pair of sampling arrays has elements at all integer multiples of T, regardless of how large M and N are. This implies that any application which depends only on second order statistics, such as angle of arrival estimation, beamforming, and multiple frequency detection, can be carried out at high resolution with the help of sparse sampling arrays. One manifestation is that two sensor arrays withM and N sensors can actually identify O(MN) independent sources. This paper extends these results to the case of multidimensional signals. The multidimensional sampling arrays operate on a lattice geometry. The coarray of such a system is studied. Even though the two lattice arrays are sparse (with respect to the integer grid), the coarray contains all integer vectors. It is also shown how to achieve the effect of a high resolution multidimensional DFT filter bank by combining coprime low resolution filter banks.", "doi": "10.1109/DSP-SPE.2011.5739252", "isbn": "978-1-61284-226-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2011-01", "pages": "425-430" }, { "id": "authors:3jf6a-nqt39", "collection": "authors", "collection_id": "3jf6a-nqt39", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120416-080128658", "type": "book_section", "title": "Coprime Sampling and the Music Algorithm", "book_title": "2011 IEEE Digital Signal Processing Workshop/IEEE Signal Processing Education Workshop (DSP/SPE)", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "A new approach to super resolution line spectrum estimation in both temporal and spatial domain using a coprime pair of samplers is proposed. Two uniform samplers with sample spacings MT and NT are used where M and N are coprime and T has the dimension of space or time. By considering the difference set of this pair of sample spacings (which arise naturally in computation of second order moments), sample locations which are O(MN) consecutive multiples of T can be generated using only O(M + N) physical samples. In order to efficiently use these O(MN) virtual samples for super resolution spectral estimation, a novel algorithm based on the idea of spatial smoothing is proposed, which can be used for estimating frequencies of sinusoids buried in noise as well as for estimating Directions-of-Arrival (DOA) of impinging signals on a sensor array. This technique allows us to construct a suitable positive semidefinite matrix on which subspace based algorithms like MUSIC can be applied to detect O(MN) spectral lines using only O(M + N) physical samples.", "doi": "10.1109/DSP-SPE.2011.5739227", "isbn": "978-1-61284-226-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2011-01", "pages": "289-294" }, { "id": "authors:swgah-vma33", "collection": "authors", "collection_id": "swgah-vma33", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170309-145320715", "type": "book_section", "title": "A novel structure for MMSE transceivers over slowly time-varying channels", "book_title": "2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Liu", "given_name": "Chih-Hao", "clpid": "Liu-Chih-Hao" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper addresses the design problem of decision feedback (DF) transceiver without zero-forcing constraint over slowly time-varying narrowband multi-input multi-output (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) is applied for the design of minimum mean square error (MMSE) DF transceiver. With space-time powerloading, the proposed space-time geometric mean decomposition (ST-GMD) MMSE transceiver maximizes Gaussian mutual information over the equivalent channel seen by each space-time block. For practical applications, the causal ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic bit error rate (BER) performance with the ST-GMD MMSE system is also developed. In high signal to interference plus noise ratio (SINR) region, our results show that the proposed MMSE transceivers have better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are a non-increasing function of the ST-block size.", "doi": "10.1109/ACSSC.2010.5757788", "isbn": "978-1-4244-9721-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2010-11", "pages": "1508-1512" }, { "id": "authors:ecf7y-3aj38", "collection": "authors", "collection_id": "ecf7y-3aj38", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170315-173417562", "type": "book_section", "title": "Efficient frequency invariant beamforming using virtual arrays", "book_title": "2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In wideband array processing, frequency invariant beamforming provides a popular means to make the beampattern allpass with respect to frequency. Traditionally, such beampatterns are realized as a two dimensional filter, using tapped delay-line (TDL) filters following each spatial sensor. However it has been recently shown that with the help of a rectangular antenna array, it is possible to generate fixed frequency invariant beampatterns without using filters. In this paper, this concept is generalized to the case of two dimensional arrays with elements on a (possibly nonseparable) lattice. Since performance of the frequency invariant beamformer depends on the number of sensors which could be large for a 2D array of size M \u00d7 N, a novel approach to beamforming based on the difference co-array of a physical array is also proposed, which avoids use of additional physical sensors. The realization of the frequency invariant beams using second order statistics of the impinging signal with only M + N physical sensors, instead of the two dimensional array of size M\u00d7N, is demonstrated. The usefulness of the proposed method is verified through computer simulation.", "doi": "10.1109/ACSSC.2010.5757573", "isbn": "978-1-4244-9721-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2010-11", "pages": "1097-1101" }, { "id": "authors:zn0hj-y2e46", "collection": "authors", "collection_id": "zn0hj-y2e46", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170309-144510721", "type": "book_section", "title": "Frequency dependent GTD coders", "book_title": "2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-Ching-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper proposes the frequency dependent generalized triangular decomposition (FDGTD) coder family for wide-sense-stationary (WSS) vector processes. Under the uniform bit allocation constraint, a set of necessary and sufficient conditions for FDGTD's coding gain optimality is derived. It is shown that one member in the FDGTD family, the frequency dependent geometric mean decomposition (FDGMD) coder, satisfies these conditions and thus is optimal. It is also demonstrated that the FDGMD coders use a simpler uniform quantizer structure and yet achieve a better performance than the conventional optimal orthonormal subband coders with sophisticated bit allocation scheme.", "doi": "10.1109/ACSSC.2010.5757621", "isbn": "978-1-4244-9721-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2010-11", "pages": "553-557" }, { "id": "authors:szg09-v5372", "collection": "authors", "collection_id": "szg09-v5372", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110330-113248959", "type": "book_section", "title": "Beamforming Using Passive Nested Arrays of Sensors", "book_title": "Proceedings of the 2010 IEEE International Symposium on Circuits and Systems (ISCAS)", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "A novel approach to beamforming using a new class of sensor arrays is proposed, which can increase the achievable\ndegrees of freedom significantly beyond the conventional limits obtained from uniform linear arrays (ULA). This class of arrays is named as \"nested arrays\" since they are obtained by nesting two or more ULAs with increasing inter-sensor spacing. Using the second order statistics of the signal received by such an array in a novel way, it is possible to perform beamforming with O(N^2) degrees of freedom using only O(N) physical elements. This kind of beamforming will be shown to be essentially non linear in nature and theoretically, it is capable of nulling the\neffect of noise provided enough snapshots are available.", "doi": "10.1109/ISCAS.2010.5536971", "isbn": "978-1-4244-5308-5", "publisher": "IEEE", "place_of_publication": "New York", "publication_date": "2010-08-03", "pages": "2840-2843" }, { "id": "authors:9xcwx-gz074", "collection": "authors", "collection_id": "9xcwx-gz074", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170309-143905742", "type": "book_section", "title": "Block diagonal GMD for zero-padded MIMO frequency selective channels with zero-forcing DFE", "book_title": "2010 IEEE International Conference on Acoustics, Speech and Signal Processing", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-Ching-Chih" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In the class of systems with linear precoder and zero-forcing (ZF) DFE for zero-padded MIMO frequency selective channels, existing optimal transceiver designs present two major drawbacks. First, the optimal system requires a large number of bits to encode the full precoding matrix. Second, the full precoding matrix leads to complex computations. These disadvantages become more severe as bandwidth (BW) efficiency increases. In this article, we propose using the block diagonal geometric mean decomposition (BD-GMD) technique to design an alternative transceiver. The proposed ZF-BD-GMD system uses a block diagonal orthogonal precoder matrix structure to reduce the required number of encoding bits and simplifies the computation. While solving the current optimal system's drawbacks, the ZF-BD-GMD system also produces a similar bit error rate (BER) performance when the block size is large. In other words, the ZF-BD-GMD system is asymptotically optimal in the class of communication systems with linear precoder and ZF-DFE receiver.", "doi": "10.1109/ICASSP.2010.5496060", "isbn": "978-1-4244-4295-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2010-03", "pages": "3202-3205" }, { "id": "authors:9wfzb-bep86", "collection": "authors", "collection_id": "9wfzb-bep86", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110412-134216292", "type": "book_section", "title": "ZF-DFE transceiver design for time-varying MIMO channels using space-time generalized triangular decomposition", "book_title": "2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Liu", "given_name": "Chih-Hao", "clpid": "Liu-Chih-Hao" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We consider the design of MIMO transceivers with zeroforcing\n(ZF) decision feedback detection over time-varying\nMIMO channels. The data vectors are grouped into spacetime\nblocks (ST-blocks) for the spatial and temporal precoding\nto take advantage of the diversity offered by time-varying\nchannels. We extend the generalized triangular decomposition\n(GTD) for the case of time-varying channels by introducing\nthe space-time GTD (ST-GTD). Based on ST-GTD\nand the channel prediction, we propose the space-time geometric\nmean decomposition (ST-GMD) based system which\nminimizes the arithmetic mean square error (MSE) for every\nST-block. We also present the causal ST-GTD based system\nwhich does not require channel prediction. The simulations\nshow that this system achieves the same BER performance\nasymptotically as the ST-GMD based system. In moderate\nhigh SNR, the proposed systems have superior BER performance\nover the conventional GMD-based systems.", "doi": "10.1109/ICASSP.2010.5496096", "isbn": "978-1-4244-4296-6", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2010", "pages": "3074-3077" }, { "id": "authors:p8a6h-h1s14", "collection": "authors", "collection_id": "p8a6h-h1s14", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110331-112637710", "type": "book_section", "title": "Active beamforming with interpolated FIR filtering", "book_title": "2010 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-C-C" } ], "abstract": "The interpolated FIR (IFIR) radar was recently\nintroduced in the context of MIMO radar theory. It was shown\nthat this system has a signal to clutter ratio intermediate between\nthose of the SIMO and MIMO radars. This paper considers\nthe optimal design of the active IFIR beamformer in presence\nof jammers. It is shown that this beamformer can achieve\nbeamwidths as sharp as those of colocated MIMO radars with\nfull-length virtual arrays. At the same time, the extra complexity\nof MIMO radars, which arises from use of multiple transmitter\nwaveforms and several sets of receiver matched filter banks, is not\npresent in the IFIR realization. Design examples for IFIR radars\nwhich optimize the receiver beamforming weights in presence of\njammers for fixed transmitter are also presented.", "doi": "10.1109/ISCAS.2010.5538007", "isbn": "978-1-4244-5308-5", "publisher": "IEEE", "place_of_publication": "New York, NY", "publication_date": "2010", "pages": "173-176" }, { "id": "authors:rcxjt-tgf13", "collection": "authors", "collection_id": "rcxjt-tgf13", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110329-111543868", "type": "book_section", "title": "ZF-DFE Transceiver for Time-varying MIMO Channels with Channel-independent Temporal Precoder", "book_title": "2010 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Liu", "given_name": "Chih-Hao", "clpid": "Liu-Chih-Hao" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper considers the DFE transceiver optimization\nfor time-varying memoryless MIMO channels under zero-forcing\n(ZF) constraint. For time-varying channels, the uncoded\naverage BER of the conventional geometric mean decomposition\n(GMD) based systems is not minimized because of the\ndiverse arithmetic MSEs at different block times. To minimize\nthe BER, a new GMD transceiver is proposed, in which the\ndata vectors are grouped into space-time blocks (ST-blocks).\nA channel independent-temporal precoder is superimposed on\nthe conventional blockwise GMD for the equalization of arithmetic\nMSEs across different blocks. So, the proposed system\ncan take advantage of both the temporal and spatial diversity\noffered by time-varying MIMO channels. At moderate high\nSNR, corresponding to reasonable BER, there exists a class\nof optimal channel-independent temporal precoders, e.g., DFT\nand Hadamard matrices, for the minimization of average BER.\nFurthermore, simulation results show that the average BER\nperformance of the proposed system improves with ST-block size\nand converges at moderate ST-block size.", "doi": "10.1109/ISCAS.2010.5537823", "isbn": "978-1-4244-5308-5", "publisher": "IEEE", "place_of_publication": "New York, NY", "publication_date": "2010", "pages": "3525-3528" }, { "id": "authors:3f3fb-ke743", "collection": "authors", "collection_id": "3f3fb-ke743", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110413-085020578", "type": "book_section", "title": "A novel array structure for directions-of-arrival estimation with increased degrees of freedom", "book_title": "2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "A novel array structure for significantly increasing the degrees\nof freedom of linear arrays is proposed. This structure\nis obtained by systematically nesting two or more uniform\nlinear arrays and can provide O(N^2) degrees of freedom using\nonly O(N) physical sensors. It is possible to provide\nclosed form expressions for the sensor locations and the exact\ndegrees of freedom obtainable from the proposed array as a\nfunction of the total number of sensors. This cannot be done\nfor existing classes of arrays like minimum redundancy arrays\nwhich have been used earlier for detecting more sources\nthan sensors. A novel spatial smoothing based technique is\nalso proposed to exploit the increased degrees of freedom offered\nby the array to perform DOA estimation of more sources\nthan sensors, using only second order statistics of the received\ndata. This method does not suffer from inherent weaknesses\nof techniques employing higher order statistics or quasi stationarity\nof sources. The validity of all the proposed methods\nis verified through numerical examples.", "doi": "10.1109/ICASSP.2010.5496268", "isbn": "978-1-4244-4296-6", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2010", "pages": "2606-2609" }, { "id": "authors:mk5y9-ym124", "collection": "authors", "collection_id": "mk5y9-ym124", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170322-172930366", "type": "book_section", "title": "Optimized DFT-FB transceivers over LTV channels", "book_title": "2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Liu", "given_name": "Chih-Hao", "clpid": "Liu-Chih-Hao" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In this work, we consider the optimization of DFT modulated filterbank transceiver (DFT-FBT) over linear time varying (LTV) channels. The DFT-FBT is a generalization of the Affine Fourier transform based OFDM (Affine OFDM) and the chirped OFDM, which are suggested in recent literature for the transmission over LTV channels. For both known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of DFT-FBT such that the signal to interference and noise ratio (SINR) at the receiver is maximized. After the optimization, the channel dependent part, like OFDM, is a set of scalar multipliers at the receiver end that adapts to the equivalent memoryless channel on a block basis. Simulation results show that the bit error rate (BER) performance of the optimized DFT-FBT over LTV channels is superior to the Affine OFDM.", "doi": "10.1109/ACSSC.2009.5470167", "isbn": "978-1-4244-5827-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2009-11", "pages": "83-87" }, { "id": "authors:hntc2-maj97", "collection": "authors", "collection_id": "hntc2-maj97", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170322-172344014", "type": "book_section", "title": "Generalized triangular transform coding", "book_title": "2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-Ching-Chih" }, { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "A general family of optimal transform coders (TC) is introduced here based on the generalized triangular decomposition (GTD) developed by Jiang, et al. This family includes the Karhunen-Loeve transform (KLT), and the prediction-based lower triangular transform (PLT) introduced by Phoong and Lin, as special cases. The coding gain of the entire family, with optimal bit allocation, is equal to those of the KLT and the PLT. Even though the PLT is not applicable for vectors which are not blocked versions of scalar wide sense stationary (WSS) processes, the GTD based family includes members which are natural extensions of the PLT, and therefore also enjoy the so-called MINLAB structure of the PLT which has the unit noise-gain property. Other special cases of the GTD-TC are the GMD (geometric mean decomposition) and the BID (bidiagonal transform). The GMD in particular has the property that the optimal bit allocation (which is required for achieving the maximum coding gain) is a uniform allocation, thereby eliminating the need for bit allocation.", "doi": "10.1109/ACSSC.2009.5469974", "isbn": "978-1-4244-5827-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2009-11", "pages": "1227-1231" }, { "id": "authors:x5cth-dpy72", "collection": "authors", "collection_id": "x5cth-dpy72", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170328-160704054", "type": "book_section", "title": "A novel autofocusing approach for estimating directions-of-arrival of wideband signals", "book_title": "Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We propose a novel approach to the design of focusing matrices which play important role in the coherent methods for wideband direction-of-arrival estimation. We call this 'autofocusing' because unlike the conventional methods, our technique constructs the focusing matrices entirely by processing the received signal and does not require any preliminary DOA estimates. In this way, it overcomes the major drawback of the coherent methods which otherwise possess many desirable properties. Through computer simulations, the proposed method is found to exhibit satisfactory performance in comparison to the existing wideband DOA estimation algorithms.", "doi": "10.1109/ACSSC.2009.5469796", "isbn": "978-1-4244-5827-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2009-11", "pages": "1663-1667" }, { "id": "authors:t9xz9-qw737", "collection": "authors", "collection_id": "t9xz9-qw737", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100722-154735690", "type": "book_section", "title": "MIMO radar with broadband waveforms: Smearing filter banks and 2D virtual arrays", "book_title": "Conference record of the 42nd Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-Piya" }, { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" } ], "abstract": "In this paper MIMO radars with broadband\nwaveforms are considered. A time domain viewpoint is\ntaken, which allows frequency invariant beamforming\nwith a filter bank called the smearing filter bank. Motivated\nby recent work on two dimensional arrays to\nobtain frequency invariant one dimensional beams, the\ngeneration of two dimensional virtual arrays from one\ndimensional ULAs is also considered. It is also argued\nthat when the smearing filter bank is appropriately used,\nfrequency invariant 2D beams can be generated.", "doi": "10.1109/ACSSC.2008.5074389", "isbn": "978-1-4244-2940-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2009-06-12", "pages": "188-192" }, { "id": "authors:q0gd1-f5773", "collection": "authors", "collection_id": "q0gd1-f5773", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100722-150551427", "type": "book_section", "title": "Joint optimization of transceivers with decision feedback and bit loading", "book_title": "Conference record of the 42nd Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-Ching-Chih" }, { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The transceiver optimization problem for MIMO\nchannels has been considered in the past with linear receivers as\nwell as with decision feedback (DFE) receivers. Joint optimization\nof bit allocation, precoder, and equalizer has in the past been\nconsidered only for the linear transceiver (transceiver with linear\nprecoder and linear equalizer). It has also been observed that\nthe use of DFE even without bit allocation in general results in\nbetter performance that linear transceivers with bit allocation.\nThis paper provides a general study of this for transceivers\nwith the zero-forcing constraint. It is formally shown that when\nthe bit allocation, precoder, and equalizer are jointly optimized,\nlinear transceivers and transceivers with DFE have identical\nperformance in the sense that transmitted power is identical\nfor a given bit rate and error probability. The developments of\nthis paper are based on the generalized triangular decomposition\n(GTD) recently introduced by Jiang, Li, and Hager. It will be\nshown that a broad class of GTD-based systems solve the optimal\nDFE problem with bit allocation. The special case of a linear\ntransceiver with optimum bit allocation will emerge as one of\nthe many solutions.", "doi": "10.1109/ACSSC.2008.5074630", "isbn": "978-1-4244-2940-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2009-06-12", "pages": "1310-1314" }, { "id": "authors:8vepr-sq854", "collection": "authors", "collection_id": "8vepr-sq854", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100708-080541700", "type": "book_section", "title": "Per-antenna power constrained MIMO transceivers optimized for BER", "book_title": "Conference record of the 42nd Asilomar Conference on Signals, Systems and Computers : October 26-29, 2008, Pacific Grove, California", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-C-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper considers the linear transceiver optimization problem for multi-carrier multiple-input multiple-output (MIMO) channels with per-antenna power constraints. Because in practical implementations each antenna is limited individually by its equipped power amplifier, this paper adopts the more realistic per-antenna power constraints, in contrast to the conventional sum-power constraint on the transmitter antennas. Assuming perfect channel knowledge both at the transmitter and the receiver, the optimization problem can be transformed into a semi-definite program (SDP), which can be solved by convex optimization tools. Furthermore, several objective functions of the MIMO system, including average bit error rate, can also be optimized by the introduction of the majorization theory.", "doi": "10.1109/ACSSC.2008.5074628", "isbn": "978-1-4244-2940-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2009-06-12", "pages": "1300-1304" }, { "id": "authors:p9zvy-tgx74", "collection": "authors", "collection_id": "p9zvy-tgx74", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100507-154344051", "type": "book_section", "title": "Joint MIMO radar waveform and receiving filter optimization", "book_title": "Acoustics, Speech and Signal Processing, 2009", "author": [ { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The concept of MIMO (multiple-input multipleoutput)\nradar allows each transmitting antenna element to\ntransmit an arbitrary waveform. This provides extra degrees\nof freedom compared to the traditional transmit beamforming\napproach. It has been shown in the recent literature that MIMO\nradar systems have many advantages. In this paper, we consider\nthe joint optimization of waveforms and receiving filters in the\nMIMO radar when the prior information of target and clutter\nare available. A novel iterative algorithm is proposed to optimize\nthe waveforms and receiving filters such that the detection performance\ncan be maximized. The proposed algorithm guarantees\nthat the SINR performance improves in each iteration step. The\nnumerical results show that the proposed methods have better\nSINR performances than existing design methods", "doi": "10.1109/ICASSP.2009.4960023", "isbn": "978-1-4244-2353-8", "publisher": "IEEE", "publication_date": "2009-04", "pages": "2073-2076" }, { "id": "authors:j6grm-brf09", "collection": "authors", "collection_id": "j6grm-brf09", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100510-100846863", "type": "book_section", "title": "Frequency invariant MVDR beamforming without filters and implementation using MIMO radar", "book_title": "Acoustics, Speech and Signal Processing, 2009", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Frequency invariant beamforming with sensor arrays is generally achieved using filters in the form of tapped delay-lines following each sensor. However it has been recently shown that with the help of the rectangular smart antenna array, it is possible to generate frequency invariant beampattern without using filters. In this paper, this frequency invariant beamforming technique is utilized to perform MVDR beamforming in the beamspace by designing frequency invariant beams spanning the desired range of azimuthal angles and optimally combining them. However, the performance of the frequency invariant beamformer depends on the number of sensors which could be large for a rectangular array of size M \u00d7 N. Making use of the virtual array concept used in MIMO radar, a novel method of producing the same frequency invariant beam, using only M transmitting and N receiving antennas, is proposed and a design example is provided to demonstrate the idea.", "doi": "10.1109/ICASSP.2009.4960025", "isbn": "978-1-4244-2353-8", "publisher": "IEEE", "publication_date": "2009-04", "pages": "2081-2084" }, { "id": "authors:8z62v-3p712", "collection": "authors", "collection_id": "8z62v-3p712", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100614-092659607", "type": "book_section", "title": "GTD-based transceivers for decision feedback and bit loading", "book_title": "International Conference on Acoustics Speech and Signal Processing (ICASSP)", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-Ching-Chih" }, { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We consider new optimization problems for transceivers with DFE receivers and linear precoders, which also use bit loading at the transmitter. First, we consider the MIMO QoS (quality of service) problem, which is to minimize the total transmitted power when the bit rate and probability of error of each data stream are specified. The developments of this paper are based on the generalized triangular decomposition (GTD) recently introduced by Jiang, Li, and Hager. It is shown that under some multiplicative majorization conditions there exists a custom GTD-based transceiver which achieves the minimal power. The problem of maximizing the bit rate subject to the total power constraint and given error probability is also considered in this paper. It is shown that the GTD-based systems also give the optimal solutions to the bit rate maximization problem.", "doi": "10.1109/ICASSP.2009.4960170", "isbn": "978-1-4244-2353-8", "publisher": "IEEE", "publication_date": "2009-04", "pages": "2661-2664" }, { "id": "authors:1qgdm-a9m35", "collection": "authors", "collection_id": "1qgdm-a9m35", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180802-134225229", "type": "book_section", "title": "Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property", "book_title": "Fundamental Papers in Wavelet Theory", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Heil", "given_name": "Christopher", "clpid": "Heil-C" }, { "family_name": "Walnut", "given_name": "David F.", "clpid": "Walnut-D-F" } ], "abstract": "[no abstract]", "doi": "10.1515/9781400827268.94", "isbn": "978-1-4008-2726-8", "publisher": "Princeton University Press", "place_of_publication": "Princeton, NJ", "publication_date": "2009-01", "pages": "94-110" }, { "id": "authors:re8yr-6j809", "collection": "authors", "collection_id": "re8yr-6j809", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100511-142143456", "type": "book_section", "title": "Transceiver design with vector perturbation technique and iterative power loading", "book_title": "Acoustics, Speech and Signal Processing, 2009", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-C-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In this paper we consider the optimization of transceivers which use the nonlinear vector perturbation technique at the transmitter. Since the perturbation vector can be almost totally removed at the receiver, the transmitter can use this extra freedom to reduce the transmitted power while maintaining the performance. The two cases considered in this paper are linear transceivers and transceivers with decision feedback (DFE). For both cases, efficient iterative power loading algorithms are developed to reduce the average bit error rate under the total transmitted power constraint. We present simulation results showing that the proposed technique performs better than the existing state-of-the-art uniform channel decomposition (UCD) system and the vector perturbation (VP) precoder.", "doi": "10.1109/ICASSP.2009.4960079", "isbn": "978-1-4244-2353-8", "publisher": "IEEE", "publication_date": "2009", "pages": "2297-2300" }, { "id": "authors:gvv5z-0a388", "collection": "authors", "collection_id": "gvv5z-0a388", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100708-112211224", "type": "book_section", "title": "Compressed sensing in MIMO radar", "book_title": "Conference record of the 42nd Asilomar Conference on Signals, Systems and Computers : October 26-29, 2008, Pacific Grove, California", "author": [ { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Compressed sensing is a technique for efficiently sampling signals which are sparse in some transform domain. Recently, the idea of compressed sensing has been used in the radar system. When the number of targets on the range-Doppler plane is small, the target scene can be reconstructed by employing the compressed sensing techniques. In this paper, we extend this idea to the MIMO radar. In the MIMO radar, the compressed sensing technique can be used to reconstruct the target scene when the signals are sparse in the range-Doppler-angle space. To effectively reconstruct the target scene, it is required that the correlation between the target responses be small. In this paper, a waveform design method is introduced to reduce the correlations between target responses. Because of the increased dimensionality in MIMO radars as compared to phased array radars, the impact of compressed sensing will be very significant there.", "doi": "10.1109/ACSSC.2008.5074356", "isbn": "978-1-4244-2940-0", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2008-10", "pages": "41-44" }, { "id": "authors:2c8fk-m4v52", "collection": "authors", "collection_id": "2c8fk-m4v52", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100722-135837385", "type": "book_section", "title": "Blind block synchronization algorithms in cyclic prefix systems", "book_title": "2008 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Su", "given_name": "Borching", "clpid": "Su-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In orthogonal frequency division multiplexing\n(OFDM) systems, symbol synchronization is a critical step for\nsuccessful data transmission. While this task is done in most\ncurrent systems by using training symbols, a few studies have\nbeen dedicated to solving the problem blindly, that is, where\ntraining symbols are not available. Blind symbol synchronization\nproblem is especially important in many blind channel estimation\nalgorithms in the literature which assume that OFDM symbol\nsynchronization is perfect. In this paper, a broader version of the\nblind symbol synchronization problem is studied, namely, blind\nblock synchronization in cyclic-prefix (CP) systems. The proposed\nalgorithm for this broader problem covers the blind symbol\nsynchronization problem in OFDM systems. Unlike previously\nreported algorithms which are based on obtaining sufficient\nstatistics of received samples, the proposed algorithm is capable\nof identifying the correct block boundaries using much less\nreceived data in absence of noise. Simulation results of the\nproposed algorithm not only verify the declared property but also\ndemonstrate improvement in accuracy of symbol synchronization\nover previously reported algorithms in presence of noise.", "doi": "10.1109/ISCAS.2008.4541373", "isbn": "978-1-4244-2078-0", "publisher": "IEEE", "publication_date": "2008-06-13", "pages": "137-140" }, { "id": "authors:d0nyj-gkx74", "collection": "authors", "collection_id": "d0nyj-gkx74", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100623-111446796", "type": "book_section", "title": "Minimum redundancy MIMO radars", "book_title": "2008 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The multiple-input multiple-output (MIMO) radar\nconcept has drawn considerable attention recently. In the traditional\nsingle-input multiple-output (SIMO) radar system, the\ntransmitter emits scaled versions of a single waveform. However,\nin the MIMO radar system, the transmitter transmits independent\nwaveforms. It has been shown that the MIMO radar can be\nused to improve system performance. Most of the MIMO radar\nresearch so far has focused on the uniform array. However, it\nis in general a loss of optimality to assume the array to be\nuniform. In this paper, the nonuniform array design problem\nin the MIMO radar is studied. In the SIMO radar, it has been\nshown that there is a class of linear arrays which minimizes the\nnumber of redundant spacings in the array. These are called\nminimum redundancy linear arrays. It has been shown that this\nclass of arrays has excellent performance in rejection of mainlobe\ninterferences. In this paper, the idea of minimum redundancy\nlinear array is extended to the MIMO radar case. The numerical\nexamples show that the proposed minimum redundancy MIMO\nradar results in improved rejection of mainlobe interferences,\nwith negligible degradation in sidelobe interference rejection\ncapabilities.", "doi": "10.1109/ISCAS.2008.4541350", "isbn": "978-1-4244-2078-0", "publication_date": "2008-06-13", "pages": "45-48" }, { "id": "authors:1np63-6ww23", "collection": "authors", "collection_id": "1np63-6ww23", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100708-095409312", "type": "book_section", "title": "Joint optimization of transceivers with fractionally spaced equalizers", "book_title": "2008 IEEE International Conference on Acoustics, Speech and Signal Processing", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-C-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In this paper we propose a method for joint optimization of transceivers with fractionally spaced equalization (FSE). We use the effective single-input multiple-output (SIMO) model for the fractionally spaced receiver. Since the FSE is used at the receiver, the optimized precoding scheme should be changed correspondingly. Simulation shows that the proposed method demonstrates remarkable improvement for jointly optimal linear transceivers as well as transceivers with decision feedback.", "doi": "10.1109/ICASSP.2008.4518259", "isbn": "978-1-4244-1483-3", "publisher": "IEEE", "publication_date": "2008-05-12", "pages": "2913-2916" }, { "id": "authors:p27sy-5sb50", "collection": "authors", "collection_id": "p27sy-5sb50", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100820-135529757", "type": "book_section", "title": "MIMO Radar Ambiguity Optimization Using Frequency-Hopping Waveforms", "book_title": "Conference Record of the Forty-first Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Chen", "given_name": "Chun-yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Matthews", "given_name": "Michael B.", "clpid": "Matthews-M-B" } ], "abstract": "Recently, the concept of MIMO (multiple-input-multiple-\noutput) radars has drawn considerable attention. In\ntraditional SIMO (single-input-multiple-output) radar, the transmitters\nemit coherent waveforms to form a focused beam. In\nMIMO radar, the transmitters emit orthogonal (or incoherent)\nwaveforms to increase the spatial resolution. These waveforms\nalso affect the range and Doppler resolution which can be\ncharacterized by the ambiguity function. In traditional (SIMO)\nradars, the ambiguity function of the transmitted pulse characterizes\nthe compromise between range and Doppler resolutions.\nIn the MIMO radar, since many transmitting waveforms are\ninvolved, their cross-ambiguity functions enter into the signal\ndesign problem. In this paper, frequency hopping codes are used\nto generate these orthogonal MIMO radar waveforms. A new\nalgorithm for designing the frequency hopping codes is proposed.\nThis algorithm makes the energy in the corresponding ambiguity\nfunctions evenly spread in the range and angular dimensions.", "doi": "10.1109/ACSSC.2007.4487193", "isbn": "978-1-4244-2109-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2008-04-11", "pages": "192-196" }, { "id": "authors:yw60e-we988", "collection": "authors", "collection_id": "yw60e-we988", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100629-080206035", "type": "book_section", "title": "Properties of the MIMO radar ambiguity function", "book_title": "2008 IEEE International Conference on Acoustics, Speech and Signal Processing", "author": [ { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "MIMO (multiple-input multiple-output) radar is an emerging technology which has drawn considerable attention. Unlike the traditional SIMO (single-input multiple-output) radar, which transmits scaled versions of a single waveform in the antenna elements, the MIMO radar transmits independent waveforms in each of the antenna elements. It has been shown that MIMO radar systems have many advantages such as high spatial resolution, improved parameter identifiability, and enhanced flexibility for transmit beampattern design. In the traditional SIMO radar, the range and Doppler resolutions can be characterized by the radar ambiguity function. It is a major tool for studying and analyzing radar signals. Recently, the ambiguity function has been extended to the MIMO radar case. In this paper, some mathematical properties of the MIMO radar ambiguity function are derived. These properties provide insights into the MIMO radar waveform design.", "doi": "10.1109/ICASSP.2008.4518108", "isbn": "978-1-4244-1483-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2008", "pages": "2309-2312" }, { "id": "authors:z855e-pkq30", "collection": "authors", "collection_id": "z855e-pkq30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101101-090318931", "type": "book_section", "title": "On the degree of MIMO systems", "book_title": "2007 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "MIMO channels and wireless communications\nsystems have generated a great deal of renewed\ninterest in linear system theory. This paper presents two\nresults. The first is a simple proof based on first principles,\nof the known fact that the McMillan degree of a causal\nM\u00d7M MIMO system is at least as large as the degree of\nits determinant. The second is a new result which shows\nthat the degree of the M\u00d7M system z^(\u22121) G(z) is equal\nto the degree of G(z) plus M if and only if the causal\nsystem G(z) has an anticausal inverse.", "doi": "10.1109/ISCAS.2007.377895", "isbn": "978-1-4244-0920-4", "publisher": "IEEE", "publication_date": "2007-06-25", "pages": "661-664" }, { "id": "authors:mg41w-21y85", "collection": "authors", "collection_id": "mg41w-21y85", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOOicassp07b", "type": "book_section", "title": "Fast search of sequences with complex symbol correlations using profile context-sensitive HMMS and pre-screening filters", "book_title": "IEEE International Conference on Acoustics, Speech and Signal Processing, 2007 (ICASSP 2007), Honolulu, HI, 15-20 April 2007", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Recently, profile context-sensitive HMMs (profile-csHMMs) have been proposed which are very effective in modeling the common patterns and motifs in related symbol sequences. Profile-csHMMs are capable of representing long-range correlations between distant symbols, even when these correlations are entangled in a complicated\nmanner. This makes profile-csHMMs an useful tool in computational biology, especially in modeling noncoding RNAs (ncRNAs) and finding new ncRNA genes. However, a profile-csHMM based search is quite slow, hence not practical for searching a large database. In this paper, we propose a practical scheme for making the search speed significantly faster without any degradation in the\nprediction accuracy. The proposed method utilizes a pre-screening filter based on a profile-HMM, which filters out most sequences that will not be predicted as a match by the original profile-csHMM. Experimental results show that the proposed approach can make the search speed eighty times faster.", "doi": "10.1109/ICASSP.2007.366687", "isbn": "1424407281", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2007-04-01", "pages": "I-345-I-348" }, { "id": "authors:jjb2r-hqt46", "collection": "authors", "collection_id": "jjb2r-hqt46", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170419-165343913", "type": "book_section", "title": "New Algorithms for Blind Block Synchronization in Zero-Padding Systems", "book_title": "2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07", "author": [ { "family_name": "Su", "given_name": "Borching", "clpid": "Su-Borching" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Blind channel identification using linear redundant filterbank precoders (LRP) has been studied extensively in the literature. Most methods are proposed based on the assumption that block synchronization is perfect. In practice, a blind block synchronization algorithm must be used to justify this assumption. This paper studies the blind block synchronization problem in systems using a zero-padding (ZP) precoder. A previously reported method is reviewed and a new approach for the problem is proposed. Generalized versions of both approaches are then developed using a parameter called repetition index. Simulation results show that when the repetition index is chosen to be greater than unity, the block synchronization error rate performance of the proposed algorithm has a significant improvement over the previously reported method.", "doi": "10.1109/ICASSP.2007.366516", "isbn": "1-4244-0727-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2007-04", "pages": "237-240" }, { "id": "authors:njp7b-n9f51", "collection": "authors", "collection_id": "njp7b-n9f51", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170419-171806680", "type": "book_section", "title": "A Subspace Method for MIMO Radar Space-Time Adaptive Processing", "book_title": "2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07", "author": [ { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In the traditional transmitting beamforming radar system, the transmitting antennas send coherent waveforms which form a highly focused beam. In the MIMO radar system, the transmitter sends noncoherent (possibly orthogonal) broad (possibly omnidirectional) waveforms. These waveforms can be extracted by a matched interbank. The extracted signals can be used to obtain more diversity or improve the clutter resolution. In this paper, we focus on space-time adaptive processing (STAP) for MIMO radar systems which improves the clutter resolution. With a slight modification, STAP methods for the SIMO radar case can also be used in MIMO radar. However, in the MIMO radar, the rank of the jammer-and-clutter subspace becomes very large, especially the jammer subspace. It affects both the complexity and the convergence of the STAP. In this paper, a new subspace method is proposed. It computes the clutter subspace using the geometry of the problem rather than data and utilizes the block diagonal property of the jammer covariance matrix. Because of fully utilizing the geometry and the structure of the covariance matrix, the method is very effective for STAP in MIMO radar.", "doi": "10.1109/ICASSP.2007.366388", "isbn": "1-4244-0727-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2007-04", "pages": "925-928" }, { "id": "authors:w2sj0-xb522", "collection": "authors", "collection_id": "w2sj0-xb522", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170424-172815266", "type": "book_section", "title": "Some properties of IIR power-symmetric filters", "book_title": "2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Power-symmetric IIR filters have in the past been used in two-channel filter banks. If appropriately designed, such filters have allpass polyphase components, and this induces useful properties in the filter bank. For example, IIR orthonormal filter banks have in the past been designed in this way, and generate orthonormal basis functions. In this paper we study some theoretical properties of IIR power symmetric filters in a more general perspective. This includes the derivation of a general analytical form, and a study of pole locations.", "doi": "10.1109/ICASSP.2007.367120", "isbn": "1-4244-0727-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2007-04", "pages": "1449-1452" }, { "id": "authors:49wk3-t5w80", "collection": "authors", "collection_id": "49wk3-t5w80", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101019-100213140", "type": "book_section", "title": "A Simple Proof of the Alternation Theorem", "book_title": "Conference Record of the Forty-first Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Nguyen", "given_name": "T. Q.", "clpid": "Nguyen-T-Q" } ], "abstract": "A simple proof of the alternation theorem for minimax FIR filter design is presented in this paper. It requires no background on mathematical optimization theory, and is based on easily understood properties of filters with equiripple behavior. The method is similar to the classical counting argument used in early mathematics literature. The contribution here is a simplified presentation which directly uses filter design language.", "doi": "10.1109/ACSSC.2007.4487395", "isbn": "978-1-4244-2109-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2007", "pages": "1111-1115" }, { "id": "authors:p8mfa-w4e19", "collection": "authors", "collection_id": "p8mfa-w4e19", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101019-100444789", "type": "book_section", "title": "A Semi-Blind Pilot-Assisted Channel Estimation Algorithm in OFDM Systems", "book_title": "Conference Record of the Forty-first Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Su", "given_name": "Borching", "clpid": "Su-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In this paper we study a new semi-blind channel estimation algorithm in orthogonal frequency division multiplexing (OFDM) systems. The proposed scheme is an extension of a recently reported subspace-based blind channel estimation algorithm in cyclic prefix systems which requires very few received blocks. The semi-blind estimation algorithm is devised by using the information obtained both from the blind channel estimation method and a pure pilot-assisted method. The proposed algorithm uses a small amount of received data and can be applied to any types of communication constellations. Simulation results show that, with the same number of pilot samples, the semi-blind algorithm has a clear improvement in system performance over the pure pilot-assisted method. To achieve the same bit- error-rate performance, the proposed semi-blind algorithm uses fewer pilot samples.", "doi": "10.1109/ACSSC.2007.4487536", "isbn": "978-1-4244-2109-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2007", "pages": "1763-1767" }, { "id": "authors:qmvw1-den23", "collection": "authors", "collection_id": "qmvw1-den23", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100825-133532010", "type": "book_section", "title": "Fast Structural Similarity Search of Noncoding RNAs Based on Matched Filtering of Stem Patterns", "book_title": "Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Matthews", "given_name": "Michael B.", "clpid": "Matthews-M-B" } ], "abstract": "Many noncoding RNAs (ncRNAs) have characteristic secondary structures that give rise to complicated base correlations in their primary sequences. Therefore, when performing an RNA similarity search to find new members of a ncRNA family, we need a statistical model - such as the profile- csHMM or the covariance model (CM) - that can effectively describe the correlations between distant bases. However, these models are computationally expensive, making the resulting RNA search very slow. To overcome this problem, various prescreening methods have been proposed that first use a simpler model to scan the database and filter out the dissimilar regions. Only the remaining regions that bear some similarity are passed to a more complex model for closer inspection. It has been shown that the prescreening approach can make the search speed significantly faster at no (or a slight) loss of prediction accuracy. In this paper, we propose a novel prescreening method based on matched filtering of stem patterns. Unlike many existing methods, the proposed method can prescreen the database solely based on structural similarity. The proposed method can handle RNAs with arbitrary secondary structures, and it can be easily incorporated into various search methods that use different statistical models. Furthermore, the proposed approach has a low computational cost, yet very effective for prescreening, as will be demonstrated in the paper.", "doi": "10.1109/ACSSC.2007.4487161", "isbn": "978-1-4244-2109-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2007", "pages": "44-48" }, { "id": "authors:sc4pk-3k310", "collection": "authors", "collection_id": "sc4pk-3k310", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101018-111516115", "type": "book_section", "title": "On equalization of channels with ZP precoders", "book_title": "2007 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In communication systems which used filter bank precoders with zero padding (ZP) at the transmitter, the effect of an FIR channel can be equalized without the use of IIR equalizers. In this paper a number of observations are made with regard to the noise gain created by the equalizer at the receiver. If the number of received samples per block actually utilized in equalization is reduced to the number of transmitted samples per block, then the noise gain can be very large for channels with zeros outside the unit circle. As the number of utilized received samples increases the situation improves. Most importantly, it is shown that when all the redundant samples in each block are utilized for estimation of transmitted symbols then the noise gain is not sensitive to whether the channel zeros are inside, on, or outside the unit circle, and depends only on the FIR channel autocorrelation", "doi": "10.1109/ISCAS.2007.378417", "isbn": "978-1-4244-0920-4", "publisher": "IEEE", "publication_date": "2007", "pages": "1329-1332" }, { "id": "authors:ddv7d-w4g54", "collection": "authors", "collection_id": "ddv7d-w4g54", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101105-105109822", "type": "book_section", "title": "On the Persistency of Excitation for Blind Channel\n Estimation in Cyclic Prefix Systems", "book_title": "2007 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Su", "given_name": "Borching", "clpid": "Su-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Recently, a new subspace-based blind channel estimation\nalgorithm in cyclic prefix (CP) system was reported.\nA persistency of excitation (PE) property of the input signal is\nrequired for the algorithm to work. In this paper, the probability\nof fulfilling the PE property under different situations is studied.\nFour factors in the algorithm affect the PE property of the input\nsignal: 1) signal constellation used; 2) precoder coefficients; 3)\nnumber of consecutive blocks; 4) a number called the repetition\nindex. Theoretical derivations as well as numerical simulations\nare given to demonstrate the main points of this paper. Important\nconclusions are 1) that the probability of fulfilling the PE\nproperty increases and converges to unity when the number\nof received blocks increases but is always upper-bounded by\na value less than unity when the repetition index increases;\n2) that the probability of fulfilling the PE property is smaller\nwhen the algorithm is applied in orthogonal frequency division\nmultiplexing (OFDM) systems than in single-carrier-cyclic-prefix\n(SC-CP) systems.", "doi": "10.1109/ISCAS.2007.378345", "isbn": "978-1-4244-0920-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2007", "pages": "1899-1902" }, { "id": "authors:gzp3p-dcq55", "collection": "authors", "collection_id": "gzp3p-dcq55", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170427-164505483", "type": "book_section", "title": "Beamforming issues in modern MIMO Radars with Doppler", "book_title": "Fortieth Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In traditional beamforming radar systems, the transmitting antennas send coherent waveforms which form a highly focused beam. In the MIMO radar system, the transmitter sends noncoherent (possibly orthogonal) broad (possibly omni-directional) waveforms. These waveforms can be extracted by a matched filterbank at the receiver. The extracted signals can be used to obtain more diversity or improve the clutter resolution. This paper focuses on space-time adaptive processing (STAP) for MlMO radar systems which improves the clutter resolution. The size of the MIMO STAP steering vector can be much larger than the traditional SIMO STAP steering vector because of the extra dimension. An accurate estimation of clutter rank for the subspace method is developed, and is a generalization of Brennan's rule to the MIMO radar case. A data independent method for estimating the clutter subspace is also described.", "doi": "10.1109/ACSSC.2006.356579", "isbn": "1-4244-0784-2", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2006-10", "pages": "41-45" }, { "id": "authors:m7yqh-dph69", "collection": "authors", "collection_id": "m7yqh-dph69", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOOgensips06", "type": "book_section", "title": "Modeling and identification of alternative folding in regulatory RNAs using context-sensitive HMMS", "book_title": "IEEE International Workshop on Genomic Signal Processing and Statistics, 2006 (GENSIPS '06), College Station, TX, 28-30 May 2006", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Recent research on gene regulation has revealed that many noncoding RNAs (ncRNAs) are actively involved in controlling various gene-regulatory networks. For such ncRNAs, their secondary structures play crucial roles in carrying out their functions. Interestingly enough, many regulatory RNAs can choose from two alternative structures based on external factors, which enables the RNAs to regulate the expression of certain genes in an environment-dependent manner. The existence of alternative structures give rise to complex\ncorrelations in the primary sequence of the RNA. In this paper, we propose an efficient method for modeling alternative secondary structures in regulatory RNAs. The proposed method can be applied to the prediction of novel regulatory RNAs in genome sequences.", "doi": "10.1109/GENSIPS.2006.353136", "isbn": "1424403855", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2006-05-01", "pages": "21-22" }, { "id": "authors:7wz6p-94182", "collection": "authors", "collection_id": "7wz6p-94182", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOOicassp06", "type": "book_section", "title": "Profile Context-Sensitive HMMs for Probabilistic Modeling of Sequences With Complex Correlations", "book_title": "IEEE International Conference on Acoustics, Speech and Signal Processing, 2006 (ICASSP 2006), Toulouse, France, 14-19 May 2006", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The profile hidden Markov model is a specific type of HMM that is well suited for describing the common features of a set of related sequences. It has been extensively used in computational biology, where it is still one of the most popular tools. In this paper, we propose a new model called the profile context-sensitive HMM. Unlike traditional profile-HMMs, the proposed model is capable of describing complex long-range correlations between distant symbols in a consensus sequence. We also introduce a general algorithm that can be used for finding the optimal state-sequence of an observed symbol sequence based on the given profile-csHMM. The proposed model has an important application in RNA sequence analysis, especially in modeling and analyzing RNA pseudoknots.", "doi": "10.1109/ICASSP.2006.1660654", "isbn": "142440469X", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2006-05", "pages": "317-320" }, { "id": "authors:vp8qp-6bj73", "collection": "authors", "collection_id": "vp8qp-6bj73", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110810-160027488", "type": "book_section", "title": "Generalized Subspace-based Algorithms For Blind Channel Estimation In Cyclic Prefix Systems", "book_title": "40th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Su", "given_name": "Borching", "clpid": "Su-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In this paper a novel generalization of subspace- based blind channel identification methods in cyclic prefix (CP) systems is proposed. For the generalization, a new system parameter called repetition index is introduced whose value is unity for previously reported special cases. By choosing a repetition index larger than unity, the number of received blocks needed for blind identification is significantly reduced compared to all previously reported methods. This feature makes it more realistic especially in wireless environments where the channel state is usually fast-varying. Given the number of received blocks available, the minimum value of repetition index is derived. Theoretical limit allows the proposed method to perform blind identification using only three received blocks. Simulation results not only demonstrate the capability of the algorithm to perform blind identification using fewer received blocks, but also show that in some cases system performance can be improved by choosing a repetition index larger than needed. If the number of received blocks and the repetition index are optimally chosen, the proposed method outperforms previously reported special cases, especially in time-varying channel environments.", "doi": "10.1109/ACSSC.2006.355071", "isbn": "1-4244-0784-2", "publisher": "IEEE", "place_of_publication": "New York", "publication_date": "2006", "pages": "1796-1800" }, { "id": "authors:rkfnq-wqc70", "collection": "authors", "collection_id": "rkfnq-wqc70", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110307-084917820", "type": "book_section", "title": "A Novel Beamformer Robust to Steering Vector\n Mismatch", "book_title": "2006 40th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "It is well know that the performance of the minimum\nvariance distortionless response (MVDR) beamformer\nis very sensitive to steering vector mismatch because of the\nsignal cancellation. Such mismatches can occur as a result of\ndirection-of arrival (DOA) errors, local scattering, near-far spatial\nsignature mismatch, waveform distortion, source spreading,\nimperfectly calibrated arrays and distorted antenna shape.\nIn this paper, an adaptive beamformer which is robust against\nthe DOA mismatch is proposed. This method imposes two\nquadratic constraints such that the magnitude responses of two\nsteering vectors exceed unity. Then a diagonal loading method\nis used to force the magnitude responses within a range of the\narrival angles to exceed unity. The diagonal loading factor can\nbe computed systematically by a proposed algorithm. Numerical\nexamples show that this method has a significantly better SINR\nperformance compared to previously published methods (including\nthe MVDR), and a complexity comparable to the standard\nMVDR beamformer.", "doi": "10.1109/ACSSC.2006.355165", "isbn": "978-1-4244-0784-2", "publisher": "IEEE", "place_of_publication": "New York", "publication_date": "2006", "pages": "2227-2231" }, { "id": "authors:v73vk-tmv73", "collection": "authors", "collection_id": "v73vk-tmv73", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110727-144256045", "type": "book_section", "title": "Vandermonde-form Preserving Matrices And The Generalized Signal Richness Preservation Problem", "book_title": "2006 Fortieth Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Su", "given_name": "Borching", "clpid": "Su-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In this paper, a theoretical problem arising in\ndigital communications, namely the generalized signal richness\npreservation problem, is addressed and studied. In order to\nsolve the problem, a special class of square matrices, namely the\n\"Vandermonde-form preserving\" (VFP) matrices, is introduced\nand found to be highly relevant to the problem. Several properties\nof VFP matrices are studied in detail. The necessary and sufficient\nconditions of the problem have been found and a systematic proof\nis also presented.", "doi": "10.1109/ACSSC.2006.354785", "isbn": "978-1-4244-0784-2", "publisher": "IEEE", "place_of_publication": "New York", "publication_date": "2006", "pages": "438-442" }, { "id": "authors:820r8-z2c55", "collection": "authors", "collection_id": "820r8-z2c55", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110825-113705963", "type": "book_section", "title": "Extensions of the Signal Richness Preservation Problem in LTI Systems", "book_title": "2005 39th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Su", "given_name": "Borching", "clpid": "Su-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The idea of signal richness has recently been studied\nin considerable details, and the conditions on linear time invariant (LTI) systems to preserve such richness have been established. In this paper, the concept of richness is extended to practically useful classes such as bounded signals. The class of LTI systems studied for the richness preservation problem are generalized to cases including rectangular systems and infinite impulse response (IIR) systems. Structured proofs of the newly found necessary\nand sufficient conditions are also presented.", "doi": "10.1109/ACSSC.2005.1599694", "isbn": "1-4244-0131-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2005-10", "pages": "25-29" }, { "id": "authors:dy071-1v648", "collection": "authors", "collection_id": "dy071-1v648", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOOssp05", "type": "book_section", "title": "An overview of the role of context-sensitive HMMs in the prediction of ncRNA genes", "book_title": "IEEE/SP Workshop on Statistical Signal Processing,13th, Bordeaux, France, 17-20 July 2005", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Non-coding RNAs (ncRNA) are RNA molecules that function in the cells without being translated into proteins. In recent years, much evidence has been found that ncRNAs play a crucial role in various biological processes. As a result, there has been an increasing interest in the prediction of ncRNA genes. Due to the conserved secondary structure in ncRNAs, there exist pairwise dependencies between distant bases. These dependencies cannot be effectively modeled using traditional HMMs, and we need a more complex model such as the context-sensitive HMM (csHMM). In this paper, we overview the role of csHMMs in the RNA secondary structure analysis and the prediction of ncRNA genes. It is demonstrated that the context-sensitive HMMs can serve as an efficient framework for these purposes.", "doi": "10.1109/SSP.2005.1628811", "isbn": "0780394038", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2005-07-01", "pages": "1378-1383" }, { "id": "authors:j62aw-p7n53", "collection": "authors", "collection_id": "j62aw-p7n53", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOOicassp05", "type": "book_section", "title": "Optimal alignment algorithm for context-sensitive hidden Markov models", "book_title": "IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005 (ICASSP '05), Philadelphia, PA, 18-23 March 2005", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The hidden Markov model is well-known for its efficiency in modeling short-term dependencies between adjacent samples. However, it cannot be used for modeling longer-range interactions between symbols that are distant from each other. In this paper, we introduce the concept of context-sensitive HMM that is capable of modeling strong pairwise correlations between distant symbols. Based on this model, we propose a polynomial-time algorithm that can be used for finding the optimal state sequence of an observed\nsymbol string. The proposed model is especially useful in modeling palindromes, which has an important application in RNA secondary structure analysis.", "doi": "10.1109/ICASSP.2005.1416003", "isbn": "0780388747", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2005-03-01", "pages": "IV-293-IV-296" }, { "id": "authors:vpdbw-tr089", "collection": "authors", "collection_id": "vpdbw-tr089", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110812-093848912", "type": "book_section", "title": "IIR Ultra-Wideband Pulse Shaper Design", "book_title": "2005 39th Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Chen", "given_name": "Chun-Yang", "clpid": "Chen-Chun-Yang" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "This paper introduces a new method to generate an ultra-wideband (UWB) pulse to fill up the Federal Communications Commission (FCC) mask. One way to generate the pulse is by summing a weighted delayed elementary waveform (e.g., a Gaussian monocycle pulse). This method can be reduced to an FIR filter design problem. In this paper, an IIR-like method is introduced. It generates the UWB pulse using the weighted sum of not only the delayed elementary waveform but also the feedback waveforms. Allpass decomposition and lattice structures are used to reduce the complexity of the implementation. Simulation shows that the IIR based method has higher filling efficiency than the FIR based method. Simulation also shows that the impulse response of the IIR shaper decays very fast. Therefore the expected long transient created by the IIR shaper is negligible.", "doi": "10.1109/ACSSC.2005.1599726", "isbn": "1-4244-0131-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2005", "pages": "172-176" }, { "id": "authors:keq8e-jd484", "collection": "authors", "collection_id": "keq8e-jd484", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOObiocas04", "type": "book_section", "title": "RNA secondary structure prediction using context-sensitive hidden Markov models", "book_title": "IEEE International Workshop on Biomedical Circuits and Systems, 2004 (BIOCAS 2004), Singapore, 1-3 December 2004", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "It has been believed for decades, that proteins are responsible for most of the genetically important functions in all cells. Due to this reason, most of the research in molecular biology was focused on identifying genes that encode proteins, and their roles in the genetic network. Recent studies indicate that non-coding RNAs play important roles in various processes. Such ncRNA genes cannot be effectively identified using traditional gene-finders that aim at protein-coding genes. Many ncRNAs conserve their secondary structures as well as their primary sequences, which have to be taken into account when looking for ncRNA genes. In this paper, we propose a new method based on context-sensitive HMMs, which can be used for predicting\nRNA secondary structure. It is demonstrated that the\nproposed model can predict the secondary structure very accurately, at a low computational cost.", "doi": "10.1109/BIOCAS.2004.1454177", "isbn": "0780386655", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2004-12-01", "pages": "S2.7.INV-1-S2.7.INV-4" }, { "id": "authors:9zk38-9k550", "collection": "authors", "collection_id": "9zk38-9k550", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOOasilo04", "type": "book_section", "title": "HMM with auxiliary memory: a new tool for modeling RNA structures", "book_title": "Asilomar Conference on Signals, Systems and Computers, 38th, Pacific Grove, CA, 7-10 November 2004", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "For a long time, proteins have been believed to perform most of the important functions in all cells. However, recent results in genomics have revealed that many RNAs that do not encode proteins play crucial roles in the cell machinery. The so-called ncRNA genes that are transcribed into RNAs but not translated into proteins, frequently conserve their secondary structures more than they conserve their primary sequences. Therefore, in order to identify ncRNA genes, we have to take the secondary structure of RNAs into consideration. Traditional approaches that are mainly based on base-composition statistics cannot be used for modeling and identifying such structures and models with more descriptive power are required. In this paper, we introduce the concept of context-sensitive HMMs, which is capable of describing pairwise interactions between distant symbols. It is demonstrated that the proposed model can efficiently model various RNA secondary structures that are frequently observed.", "doi": "10.1109/ACSSC.2004.1399438", "isbn": "0780386221", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2004-11-01", "pages": "1651-1655" }, { "id": "authors:za3s3-a8965", "collection": "authors", "collection_id": "za3s3-a8965", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170518-114248651", "type": "book_section", "title": "Remarks on certain new methods for blind identification of FIR channels", "book_title": "Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Su", "given_name": "Borching", "clpid": "Su-Borching" } ], "abstract": "This paper discusses a number of issues pertaining to blind identification of channels. The basics of blind identification are first discussed and a method called Vandermonde method is presented which is based on elementary linear system principles. Then some remarks are made about precoders with paraunitary antipodal preprocessors. It is argued that such preprocessors usually destroy signal richness which is a necessary feature in blind identification systems.", "doi": "10.1109/ACSSC.2004.1399254", "isbn": "0-7803-8622-1", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2004-11", "pages": "832-836" }, { "id": "authors:r63qe-z5j47", "collection": "authors", "collection_id": "r63qe-z5j47", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOOiscas04", "type": "book_section", "title": "Discrete pdf estimation in the presence of noise", "book_title": "International Symposium on Circuits and Systems, 2004, (ISCAS '04), Vancouver, British Columbia, 23-26 May 2004", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The problem of estimating a pdf from measurements has been widely studied by many researchers. However, most of the work was focused on estimating a probability density function of continuous random variables, especially in the absence of noise. In this paper, we consider a model for representing discrete probability density functions based on multirate dsp models. Using this model, we propose an efficient and stable scheme for pdf estimation\nwhen the measurements are corrupted by independent additive\nnoise. This approach makes use of well-known results from multirate dsp theory, especially that of biorthogonal partners. Simulation results are given, which clearly show the advantage of the proposed method.", "doi": "10.1109/ISCAS.2004.1328748", "isbn": "078038251X", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2004-09-03", "pages": "III-321" }, { "id": "authors:vr95t-bha29", "collection": "authors", "collection_id": "vr95t-bha29", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOOdwpws04", "type": "book_section", "title": "Identification of CpG islands using a bank of IIR lowpass filters", "book_title": "IEEE Digital Signal Processing Workshop,11th, and the 3rd IEEE Signal Processing Education Workshop, Taos Ski Valley, NM, 1-4 August 2004", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "It has been known that biological sequences such as the DNA sequence display different kinds of patterns depending on their biological functions. This statistical difference can be exploited for identifying the region of interest, such as the protein coding regions or CpG islands, in a new biological sequence that has not been annotated yet. A region of particular interest is the CpG island, which is a region in a DNA sequence that is rich in the dinucleotide CpG, since it is known that they can be used as gene markers. There have been several computational methods for identifying CpG islands, each with its own strength and weakness. In this paper, we propose a novel scheme for detecting CpG islands in a genomic sequence, which is based on a bank of IIR lowpass filters. The proposed method is capable of identifying CpG islands efficiently at a low computational expense. Simulation results are included where appropriate to demonstrate the idea.", "doi": "10.1109/DSPWS.2004.1437966", "isbn": "0780384342", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2004-08-01", "pages": "315-319" }, { "id": "authors:gb3b2-vkd18", "collection": "authors", "collection_id": "gb3b2-vkd18", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOOasilo03", "type": "book_section", "title": "Improved Estimation of Discrete Probability Density Functions Using Multirate Models", "book_title": "Asilomar Conference on Signals, Systems and Computers, 37th, Pacific Grove, CA, 9-12 November 2003", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "For many decades, the problem of estimating a pdf based on measurements has been of interest to many researchers. Even though much work has been done in the area of pdf estimation, most of it was focused on the continuous case. In this paper, we propose a new model based approach for estimating a discrete probability density function. This approach is based on multirate dsp theory, and it has several advantages over the traditional histogram method. It is shown that this method yields an unbiased pdf estimate\nwith small variance, which is guaranteed to have a smaller\nestimation error than the histogram. Simulation results are given, which show the merit of the proposed method.", "doi": "10.1109/ACSSC.2003.1292112", "isbn": "0780381041", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ.", "publication_date": "2004-05-04", "pages": "1188-1192" }, { "id": "authors:aa6rh-hgt54", "collection": "authors", "collection_id": "aa6rh-hgt54", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:YOOicassp04", "type": "book_section", "title": "Wavelet-based denoising by customized thresholding", "book_title": "Acoustics, Speech, and Signal Processing, 2004. Proceedings. (ICASSP '04). IEEE International Conference on", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The problem of estimating a signal that is corrupted by additive noise has been of interest to many researchers for practical as well as theoretical reasons. Many of the traditional denoising methods have been using linear methods such as the Wiener filtering. Recently, nonlinear methods, especially those based on wavelets have become increasingly popular, due to a number of advantages over the linear methods. It has been shown that wavelet-thresholding\nhas near-optimal properties in the minimax sense,\nand guarantees better rate of convergence, despite its simplicity. Even though much work has been done in the field of wavelet-thresholding, most of it was focused on statistical modeling of the wavelet coefficients and the optimal choice of the thresholds. In this paper, we propose a custom thresholding function which can improve the denoised results significantly. Simulation results are\ngiven to demonstrate the advantage of the new thresholding function.", "doi": "10.1109/ICASSP.2004.1326410", "isbn": "0780384849", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2004-05-01", "pages": "925-928" }, { "id": "authors:m7jdn-5e083", "collection": "authors", "collection_id": "m7jdn-5e083", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110907-113511682", "type": "book_section", "title": "Iterative gradient technique for the design of least squares optimal FIR magnitude squared Nyquist filters", "book_title": "2004 IEEE International Conference on Acoustics, Speech, and Signal Processing : \u01c2b proceedings : May 17-21, 2004, Fairmont Queen Elizabeth Hotel, Montreal, Quebec, Canada", "author": [ { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Recently, much attention has been given to the design of optimal finite impulse response (FIR) compaction filters. Such filters, which arise in the design of optimal signal-adapted orthonormal FIR filter banks, satisfy a magnitude squared Nyquist constraint in addition to the inherent FIR assumption. In this paper, we focus on the least squares optimal design of FIR filters whose magnitude squared response satisfies a Nyquist constraint. Using a complete characterization of such systems in terms of Householder-like building blocks, an iterative gradient based greedy algorithm is proposed to design such filters. Simulation results provided show the merit of the proposed technique for designing FIR compaction filters.", "doi": "10.1109/ICASSP.2004.1326424", "isbn": "9780780384842", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2004-05", "pages": "981-984" }, { "id": "authors:bs351-0fh66", "collection": "authors", "collection_id": "bs351-0fh66", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111013-161223340", "type": "book_section", "title": "Iterative algorithm for the design of optimal FIR analysis/synthesis filters for overdecimated filter banks", "book_title": "Proceedings of the 2004 International Symposium on Circuits and Systems", "author": [ { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Recently, much attention has been given to the design of signal-adapted filter banks, in which the filter banks are designed to optimize a particular objective function, i.e. coding gain or a multiresolution criterion, for a particular class of input signals. If we restrict the analysis/synthesis filters to satisfy an orthonormality or biorthogonality condition, but put no restrictions on filter orders, then often times it is known how to choose the filters optimally for the objectives mentioned above. However, such filters are often unrealizable infinite order filters. In this paper, we consider the design of optimal analysis/synthesis filters in which the only restriction is that they must be finite impulse response (FIR) filters. We focus here on minimizing the mean squared reconstruction error for overdecimated filter banks. An iterative method to alternately design the analysis and synthesis banks is presented in which the error is monotonic nonincreasing for each iteration. Simulation results provided show the merit of the proposed algorithm.", "doi": "10.1109/ISCAS.2004.1328749", "isbn": "0-7803-8251-X", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2004-05", "pages": "325-328" }, { "id": "authors:4j427-nk669", "collection": "authors", "collection_id": "4j427-nk669", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170705-171833899", "type": "book_section", "title": "Sampling Theorems for Nonbandlimited Signals", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Benedetto", "given_name": "John J.", "clpid": "Benedetto-J-J" }, { "family_name": "Zayed", "given_name": "Ahmed I.", "clpid": "Zayed-A-I" } ], "abstract": "In recent years many of the results for bandlimited sampling have been extended to the case of nonbandlimited signals. These recent extensions have been found to be useful in digital signal processing applications such as image interpolation, equalization of communication channels, and multiresolution computation. In this chapter we give a brief overview of some of these ideas.", "doi": "10.1007/978-0-8176-8212-5_5", "publisher": "Springer", "publication_date": "2004" }, { "id": "authors:ncqz1-7gr84", "collection": "authors", "collection_id": "ncqz1-7gr84", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111028-095213336", "type": "book_section", "title": "Iterative Eigenfilter method for designing optimum overdecimated orthonormal FIR compaction filter banks", "book_title": "Conference record of the Thirty-Seventh Asilomar Conference on Signals, Systems & Computers", "author": [ { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Mathews", "given_name": "M. B.", "clpid": "Mathews-M-B" } ], "abstract": "Much attention has recently been given to the construction of signal-adapted orthonormal filter banks designed to optimize a particular objective function such as coding gain or a multiresolution criterion. For certain classes of filter banks, the optimum solution is a principal component filter bank (PCFB), which is simultaneously optimal for several objectives including the ones mentioned above. However, for the class of finite impulse response (FIR) filter banks, a PCFB in general does not exist. For this case, numerical techniques must be employed to find an optimum filter bank for a particular objective. In this paper, we present an iterative method for designing an overdecimated FIR filter bank optimized for energy compaction. The proposed algorithm is an eigenfilter method that is low in computational complexity. Simulation results show the merit of the proposed method, in that as the filter order increases, the filters designed behave more and more like those of the infinite order PCFB.", "doi": "10.1109/ACSSC.2003.1292115", "isbn": "0-7803-8104-1", "publisher": "IEEE", "place_of_publication": "Piscataway, N.J.", "publication_date": "2003-11", "pages": "1203-1207" }, { "id": "authors:0xqvp-fsq55", "collection": "authors", "collection_id": "0xqvp-fsq55", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:VAIicme03", "type": "book_section", "title": "Discrete probability density estimation using multirate DSP models", "book_title": "International Conference on Multimedia and Expo, 2003 (ICME '03), Baltimore, MD, 6-9 July 2003", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-B-J" } ], "abstract": "We propose a model based approach for estimation of probability mass functions for discrete random variables. The model is based on tools from multirate signal processing. Similar in principle to the kernel based methods, the approach takes advantage of well-known results from multirate signal processing theory. Similarities to and differences from wavelet based approaches is also indicated where appropriate. In the final form, the probability estimates are obtained by filtering the square root of the histogram through a multirate system whose components are biorthogonal partners of each other.", "doi": "10.1109/ICME.2003.1221052", "isbn": "0-7803-7663-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2003-08-08", "pages": "VI-477-VI-480" }, { "id": "authors:pm5vc-n6m42", "collection": "authors", "collection_id": "pm5vc-n6m42", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111019-152758261", "type": "book_section", "title": "On the least squares signal approximation model for overdecimated rational nonuniform filter banks and applications", "book_title": "2003 International Conference on Multimedia and Expo", "author": [ { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "With the advent of wavelets for lossy data compression came the notion of representing signals in a certain vector space by their projections in well chosen subspaces of the original space. In this paper, we consider the subspace of signals generated by an overdecimated rational nonuniform filter bank and find the optimal conditions under which the mean-squared error between a given deterministic signal and its representation in this subspace is minimized for a fixed set of synthesis filters. Under these optimal conditions, it is shown that choosing the synthesis filters to further minimize this error is simply an energy compaction problem. With this, we introduce the notion of deterministic energy compaction filters for classes of signals. Simulation results are presented showing the merit of our proposed method for optimizing the synthesis filters.", "doi": "10.1109/ICME.2003.1221053", "isbn": "0-7803-7965-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2003-07", "pages": "857-860" }, { "id": "authors:pnrzt-2ye78", "collection": "authors", "collection_id": "pnrzt-2ye78", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170522-165550367", "type": "book_section", "title": "Filter banks for cyclic-prefixing the nonuniform DMT system", "book_title": "Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Vrcelj", "given_name": "Bojan", "clpid": "Vrcelj-B" } ], "abstract": "The cyclic prefix system is used in discrete multitone channels for frequency domain equalization and is based on the inversion of samples of the channel frequency response at uniformly spaced points (DFT coefficients). In this paper, we consider nonuniformly spaced samples of the channel frequency response, especially octave-spaced. The anticipated advantage is that for channels with rapidly decaying frequency responses, there are relatively fewer equalizer coefficients with unduly large values, and helps to reduce amplification of channel noise at the receiver. We show how to combine a wavelet-like filter bank with traditional DFTs to achieve this goal. While the idea appears to be exciting and opens up interesting problems, its merits still remain to be evaluated.", "doi": "10.1109/ACSSC.2002.1197292", "isbn": "0-7803-7576-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2002-11", "pages": "816-820" }, { "id": "authors:aa7et-2gv49", "collection": "authors", "collection_id": "aa7et-2gv49", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170522-160842755", "type": "book_section", "title": "Fractional biorthogonal partners in fractionally spaced equalizers", "book_title": "IEEE International Conference on Acoustics Speech and Signal Processing", "author": [ { "family_name": "Vrcelj", "given_name": "Bojan", "clpid": "Vrcelj-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The concept of fractional biorthogonal partners has been introduced recently by the authors. They arise in many different contexts, one of them being channel equalization with fractionally spaced equalizers. If the amount of oversampling at the receiver is not an integer, but a rational number, the problem of fractionally spaced equalization can be treated using the fractional biorthogonal partner setting. This approach is adopted here. We consider fractionally spaced equalizers with a rational amount of oversampling, show that the FIR solution (if it exists) is not unique and can be chosen to minimize the noise power at the receiver. These findings are demonstrated by examples where we compare the performance of fractionally spaced zero forcing equalizers to that of the corresponding minimum mean-squared error solution.", "doi": "10.1109/ICASSP.2002.5745102", "isbn": "0-7803-7402-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2002-05", "pages": "2289-2292" }, { "id": "authors:kybm6-h2f32", "collection": "authors", "collection_id": "kybm6-h2f32", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111110-072520331", "type": "book_section", "title": "A new eigenfilter based method for optimal design of channel shortening equalizers", "book_title": "2002 IEEE International Symposium on Circuits and Systems Proceedings", "author": [ { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Recently much attention has been given to the design of time-domain equalizers or TEQs for discrete multitone modulation (DMT) systems. We present a new method for the design of such equalizers which minimizes both the intersymbol interference (ISI) and noise power observed in a DMT system. Furthermore, we show how this method can be used for the design of fractionally spaced equalizers or FSEs. Experimental results are presented showing that our design method performs better than other known techniques in terms of achievable bit rate.", "doi": "10.1109/ISCAS.2002.1011035", "isbn": "0-7803-7448-7", "publisher": "IEEE", "place_of_publication": "Piscataway, N.J.", "publication_date": "2002-05", "pages": "504-507" }, { "id": "authors:netd6-va137", "collection": "authors", "collection_id": "netd6-va137", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111109-095832458", "type": "book_section", "title": "Eigenfilter design of MIMO equalizers for channel shortening", "book_title": "2002 IEEE International Conference on Acoustics, Speech, and Signal Processing", "author": [ { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The advent of discrete multitone modulation (DMT) systems in recent years has brought to light the importance of channel shortening equalizers. In this paper, we present a method for the design of one such equalizer for multiple-input multiple-output (MIMO) linear dispersive channels. This method is a generalization of one that was used for shortening of single-input single-output (SISO) channels. Experimental results presented show that our design method performs better than the minimum mean-squared error (MMSE) technique in terms of effective channel energy compaction.", "doi": "10.1109/ICASSP.2002.5745120", "isbn": "0-7803-7402-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2002-05", "pages": "2361-2364" }, { "id": "authors:r37s3-g5z92", "collection": "authors", "collection_id": "r37s3-g5z92", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170522-162142818", "type": "book_section", "title": "Fractional biorthogonal partners and application in signal interpolation", "book_title": "2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353)", "author": [ { "family_name": "Vrcelj", "given_name": "Bojan", "clpid": "Vrcelj-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The concept of biorthogonal partners has been introduced recently by the authors. The work presented in this paper is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers. Hence the name fractional biorthogonal partners. The conditions for the existence of stable and of FIR fractional biorthogonal partners are derived. This result gives rise to an all-FIR spline interpolation technique with the minimum amount of required oversampling. This technique is illustrated by an interpolation example.", "doi": "10.1109/ISCAS.2002.1010375", "isbn": "0-7803-7448-7", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2002-05", "pages": "9-12" }, { "id": "authors:bfk3b-yz039", "collection": "authors", "collection_id": "bfk3b-yz039", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111101-135711309", "type": "book_section", "title": "Noise optimized eigenfilter design of time-domain equalizers for DMT systems", "book_title": "2002 IEEE International Conference on Communications", "author": [ { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The design of time-domain equalizers or TEQs for discrete multitone modulation (DMT) systems has recently received much attention. In this paper, we present a generalization of one such design method which takes into account the noise observed in a DMT channel. Furthermore, we show how this generalization can be used for the design of fractionally spaced equalizers or FSEs. Experimental results are presented showing that our design method performs better than other known techniques.", "doi": "10.1109/ICC.2002.996816", "isbn": "0-7803-7400-2", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2002-04", "pages": "54-58" }, { "id": "authors:0cpd8-sm351", "collection": "authors", "collection_id": "0cpd8-sm351", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181213-143631577", "type": "book_section", "title": "New methods for digital halftoning and inverse halftoning", "book_title": "Color Imaging: Device-Independent Color, Color Hardcopy, and Applications VII", "author": [ { "family_name": "Me\u015fe", "given_name": "Murat", "clpid": "Me\u015fe-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Eschbach", "given_name": "Reiner", "clpid": "Eschbach-R" }, { "family_name": "Marcu", "given_name": "Gabriel G.", "clpid": "Marcu-G-G" } ], "abstract": "Halftoning is the rendition of continuous-tone pictures on bi-level displays. Here we first review some of the halftoning algorithms which have a direct bearing on our paper and then describe some of the more recent advances in the field. Dot diffusion halftoning has the advantage of pixel-level parallelism, unlike the popular error diffusion halftoning method. We first review the dot diffusion algorithm and describe a recent method to improve its image quality by taking advantage of the Human Visual System function. Then we discuss the inverse halftoning problem: The reconstruction of a continuous tone image from its halftone. We briefly review the methods for inverse halftoning, and discuss the advantages of a recent algorithm, namely, the Look Up Table (LUT)Method. This method is extremely fast and achieves image quality comparable to that of the best known methods. It can be applied to any halftoning scheme. We then introduce LUT based halftoning and tree-structured LUT (TLUT)halftoning. We demonstrate how halftone image quality in between that of error diffusion and Direct Binary Search (DBS)can be achieved depending on the size of tree structure in TLUT algorithm while keeping the complexity of the algorithm much lower than that of DBS.", "doi": "10.1117/12.452998", "isbn": "9780819444035", "publisher": "Society of Photo-optical Instrumentation Engineers (SPIE)", "place_of_publication": "Bellingham, WA", "publication_date": "2001-12-28", "pages": "278-292" }, { "id": "authors:31rhp-d4y96", "collection": "authors", "collection_id": "31rhp-d4y96", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170523-151633112", "type": "book_section", "title": "New sampling expansions for bandlimited signals based on chromatic derivatives", "book_title": "Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Ignjatovic", "given_name": "A.", "clpid": "Ignjatovic-A" }, { "family_name": "Narasimha", "given_name": "M. J.", "clpid": "Narasimha-M-J" } ], "abstract": "Shannon's sampling theorem for bandlimited signals has been generalized in many directions in the last few decades. These extensions lead to various types of signal representations having different sets of basis functions. One particular extension proposed by Papoulis (1977) and later developed further by Brown (1981) can be interpreted in terms of a continuous time minimally sampled filter bank. In this paper we take a second look at these filter banks and use a continuous time version of the familiar biorthogonality property to obtain further insights into these sampling theorems. This viewpoint also makes a natural connection to the theory of orthogonal polynomials. We then elaborate on an elegant representation called the chromatic derivative expansion based on the use of Chebyshev polynomials. Using this expansion, the analysis/synthesis system can be described with a Chebyshev/Bessel pair of functions.", "doi": "10.1109/ACSSC.2001.986985", "isbn": "0-7803-7147-X", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2001-11", "pages": "558-562" }, { "id": "authors:sb739-n8z22", "collection": "authors", "collection_id": "sb739-n8z22", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111117-095759825", "type": "book_section", "title": "Generalized kurtosis and applications in blind equalization of MIMO channels", "book_title": "Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems, and Computers", "author": [ { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Matthews", "given_name": "M. B.", "clpid": "Matthews-M-B" } ], "abstract": "Recently, the problem of blind equalization of multiple-input multiple-output (MIMO) channels has received much attention from the communications and signal processing communities. Several methods proposed to solve this problem involve computing the kurtosis of the components of the observed output vector sequence. In this paper, we generalize the notion of kurtosis to vector sequences by proposing a definition for a kurtosis matrix of a random vector. It is shown that there are many analogies between our kurtosis matrix and the classical scalar kurtosis. We then use this matrix to develop a necessary condition for blind equalization of MIMO channels. Future work will include the development of a sufficient condition for equalization.", "doi": "10.1109/ACSSC.2001.987023", "isbn": "0-7803-7147-X", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2001-11", "pages": "742-746" }, { "id": "authors:aq9b0-x9x21", "collection": "authors", "collection_id": "aq9b0-x9x21", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111122-142434848", "type": "book_section", "title": "Sinusoidal frequency estimation using filter banks", "book_title": "2001 IEEE International Conference on Acoustics, Speech, and Signal Processing Proceedings", "author": [ { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "One problem of great interest to the signal processing community is that of estimating the frequencies of sinusoids buried in noise. Traditional methods applied to a fullband signal fail to estimate accurately when the signal-to-noise ratio (SNR) or spacing between frequencies is small. They also fail when the noise is not white and its statistics are unknown. We consider these methods when applied to the subbands of a filter bank and show that, through proper choice of analysis filters, the local SNR and frequency spacing increase by the decimation ratio. We also show that the subband noise processes are, on average, more \"white\" than the fullband one in terms of the spectral flatness measure. This suggests that if the noise statistics are unknown, there will be less error by estimating in the subbands as opposed to the fullband. Experimental results support this theory, as we show.", "doi": "10.1109/ICASSP.2001.940311", "isbn": "0-7803-7041-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2001-05", "pages": "3089-3092" }, { "id": "authors:t9c62-7p286", "collection": "authors", "collection_id": "t9c62-7p286", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181204-132725682", "type": "book_section", "title": "Nonuniform principal component filter banks: definitions, existence, and optimality", "book_title": "Wavelet Applications in Signal and Image Processing VIII", "author": [ { "family_name": "Akkarakaran", "given_name": "Sony J.", "clpid": "Akkarakaran-S-J" }, { "family_name": "Vaidyanathan", "given_name": "Palghat P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Aldroubi", "given_name": "Akram", "clpid": "Aldroubi-A" }, { "family_name": "Laine", "given_name": "Andrew F.", "clpid": "Laine-A-F" }, { "family_name": "Unser", "given_name": "Michael A.", "clpid": "Unser-M-A" } ], "abstract": "The optimality of principal component filter banks (PCFBs) for data compression has been observed in many works to varying extents. Recent work by the authors has made explicit the precise connection between the optimality of uniform orthonormal filter banks (FBs) and the principal component property: The PCFB is optimal whenever the minimization objective is a concave function of the subband variances of the FB. This gives a unified explanation of PCFB optimality for compression, denoising and progressive transmission. However not much is known for the case when the optimization is over a class of nonuniform Fbs. In this paper we first define the notion of a PCFB for a class of nonuniform orthonormal Fbs. We then show how it generalizes the uniform PCFBs by being optimal for a certain family of concave objectives. Lastly, we show that existence of nonuniform PCFBs could imply severe restrictions on the input power spectrum. For example, for the class of unconstrained orthonormal nonuniform Fbs with any given set of decimators that are not all equal, there is no PCFB if the input spectrum is strictly monotone.", "doi": "10.1117/12.408666", "isbn": "9780819437648", "publisher": "Society of Photo-optical Instrumentation Engineers (SPIE)", "place_of_publication": "Bellingham, WA", "publication_date": "2000-12-04", "pages": "768-779" }, { "id": "authors:68jkd-v1c25", "collection": "authors", "collection_id": "68jkd-v1c25", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170523-155943925", "type": "book_section", "title": "Optimizing the capacity of orthogonal and biorthogonal DMT channels", "book_title": "10th European Signal Processing Conference", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Lin", "given_name": "Yuan-Pei", "clpid": "Lin-Yuan-Pei" }, { "family_name": "Akkarakaran", "given_name": "Sony", "clpid": "Akkarakaran-S" }, { "family_name": "Phoong", "given_name": "See-May", "clpid": "Phoong-See-May" } ], "abstract": "The uniform DFT filter bank has been used routinely in discrete multitone modulation (DMT) systems because of implementation efficiency. It has recently been shown that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT communication. In this paper we show that such filter banks are optimal even when scalar prefilters and postfilters are used around the channel. We show that the theoretically optimum scalar prefilter is the half-whitening solution, well known in data compression theory. We conclude with the observation that the PCFB continues to be optimal for the maximization of theoretical capacity as well.", "isbn": "978-952-1504-43-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2000-09" }, { "id": "authors:yv999-gba62", "collection": "authors", "collection_id": "yv999-gba62", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181204-132721745", "type": "book_section", "title": "Role of principal component filter banks in noise reduction", "book_title": "Wavelet Applications in Signal and Image Processing VII", "author": [ { "family_name": "Akkarakaran", "given_name": "Sony", "clpid": "Akkarakaran-S-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Unser", "given_name": "Michael A.", "clpid": "Unser-M-A" }, { "family_name": "Aldroubi", "given_name": "Akram", "clpid": "Aldroubi-A" }, { "family_name": "Laine", "given_name": "Andrew F.", "clpid": "Laine-A-F" } ], "abstract": "The purpose of this paper is to demonstrate the optimality properties of principal component filter-banks for various noise reduction schemes. Optimization of filter-banks (FB's) for coding gain maximization has been carried out in the literature, and the optimized solutions have been observed to satisfy the principal component property, which has independently been studied. Here we show a strong connection between the optimality and the principal component property; which allows us to optimize FB's for many other objectives. Thus, we consider the noise-reduction scheme where a noisy signal is analyzed using a FB and the subband signals are processed either using a hard-threshold operation or a zeroth order Wiener filter. For these situations, we show that a principal FB is again optimal in the sense of minimizing the expected mean-square error.", "doi": "10.1117/12.366792", "isbn": "9780819432995", "publisher": "Society of Photo-optical Instrumentation Engineers (SPIE)", "place_of_publication": "Bellingham, WA", "publication_date": "1999-10-26", "pages": "346-357" }, { "id": "authors:bsb03-34c24", "collection": "authors", "collection_id": "bsb03-34c24", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150513-083430291", "type": "book_section", "title": "Optimization of filter banks based on properties of the input signal", "book_title": "9th European Signal Processing Conference", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Filter banks and wavelets have found applications in signal compression, noise removal, and in many other signal processing contexts. In this tutorial we review a number of recent results on the optimization of filter banks based on the knowledge of the input. The main emphasis will be the minimization of error due to subband quantization, and its connection to principal component reconstruction. Both uniform and nonuniform filter banks are considered.", "isbn": "978-960-7620-06-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1998-09", "pages": "1-6" }, { "id": "authors:sbnbq-ffs66", "collection": "authors", "collection_id": "sbnbq-ffs66", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150513-121754858", "type": "book_section", "title": "Image halftoning using optimized dot diffusion", "book_title": "9th European Signal Processing Conference", "author": [ { "family_name": "Me\u015fe", "given_name": "Murat", "clpid": "Me\u015fe-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The dot diffusion method for digital halftoning has the advantage of parallelism unlike the error diffusion method. However, image quality offered by error diffusion is still regarded as superior to other known methods. In this paper we show how the dot diffusion method can be improved by optimization of the so-called class matrix. By taking the human visual characteristics into account we show that such optimization consistently results in images comparable to error diffusion, without sacrificing the parallelism.", "isbn": "978-960-7620-06-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1998-09", "pages": "1-4" }, { "id": "authors:exp6z-fhv94", "collection": "authors", "collection_id": "exp6z-fhv94", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TUQisit98", "type": "book_section", "title": "Globally optimal FIR filters with applications in source and channel coding", "book_title": "IEEE International Symposium on Information Theory, 1998. Proceedings.", "author": [ { "family_name": "Tuqan", "given_name": "Jamal", "clpid": "Tuqan-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In this paper, we derive a novel formulation to solve an important FIR filter optimization problem. The problem has received considerable attention in the past because it appears in a wide variety of disciplines. The newly proposed method finds the globally optimal solution to the problem and provides\nseveral other advantages over previous optimization techniques.", "doi": "10.1109/ISIT.1998.709080", "isbn": "0-7803-5000-6", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1998-08-01", "pages": "475" }, { "id": "authors:1ns6y-et576", "collection": "authors", "collection_id": "1ns6y-et576", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150518-100031998", "type": "book_section", "title": "Results on cyclic signal processing systems", "book_title": "9th European Signal Processing Conference (EUSIPCO 1998)", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We present a state space description for cyclic LTI systems\nwhich find applications in cyclic filter banks and wavelets. We also revisit the notions of reachability and\nobservability in the cyclic context, and show a number of\nimportant differences from traditional noncyclic case. A\nnumber of related problems such as the paraunitary interpolation problem and the cyclic paraunitary factorizability problem can be understood in a unified way by using the realization matrix defined by the state space description.", "isbn": "978-960-7620-06-4", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1998" }, { "id": "authors:f0v84-9xz81", "collection": "authors", "collection_id": "f0v84-9xz81", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TUQiscas98b", "type": "book_section", "title": "The role of the discrete-time Kalman-Yakubovitch-Popov lemma in designing statistically optimum FIR orthonormal filter banks", "book_title": "IEEE International Symposium on Circuits and Systems (ISCAS '98), Monterey, CA", "author": [ { "family_name": "Tuqan", "given_name": "Jamal", "clpid": "Tuqan-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We introduce a new approach to design FIR energy compaction filters of arbitrary order N. The optimization of such filters is important due to their close connection to the design of an M-channel orthonormal filter bank adapted to the input signal statistics. The novel procedure finds the optimum product filter Fopt(Z)=H opt(Z)Hopt(Z^-1) corresponding to the compaction filter Hopt(z). The idea is to express F(z) as D(z)+D(z^-1) and reformulate the compaction problem in terms of the state space realization of the causal function D(z). For a fixed input power spectrum, the resulting filter Fopt(z) is guaranteed to be a global optimum due to the convexity of the new formulation. The new design method can be solved quite efficiently and with great accuracy using recently developed interior point methods and is extremely general in the sense that it works for any chosen M and any arbitrary filter length N. Finally, obtaining Hopt(z) from F opt(z) does not require an additional spectral factorization step. The minimum phase spectral factor can be obtained automatically by relating the state space realization of Dopt(z) to that of H opt(z).", "doi": "10.1109/ISCAS.1998.694423", "isbn": "0780344553", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1998", "pages": "122-125" }, { "id": "authors:6s5b9-stb96", "collection": "authors", "collection_id": "6s5b9-stb96", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TUQiscas98a", "type": "book_section", "title": "The design of optimum filters for quantizing a class of non bandlimited signals", "book_title": "IEEE International Symposium on Circuits and Systems (ISCAS '98), Monterey, CA", "author": [ { "family_name": "Tuqan", "given_name": "Jamal", "clpid": "Tuqan-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We consider the efficient quantization of a class of non bandlimited signals, namely the class of discrete time signals that can be recovered from their decimated version. By definition, these signals are oversampled and it is reasonable to expect that we can reap the same benefits of well known efficient A/D conversion techniques. Indeed, by using appropriate multirate reconstruction schemes, we first show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of the signals. To further increase the effective quantizer resolution, noise shaping is introduced by optimizing linear time invariant (LTI) and linear periodically time varying (LPTV)M pre- and post-filters around the quantizer. Closed form expressions for the optimum filters and the minimum mean squared error are derived for each case.", "doi": "10.1109/ISCAS.1998.694401", "isbn": "0780344553", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1998", "pages": "33-36" }, { "id": "authors:wa453-yfw49", "collection": "authors", "collection_id": "wa453-yfw49", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180730-162432316", "type": "book_section", "title": "Review of recent results on optimal orthonormal subband coders", "book_title": "Wavelet Applications in Signal and Image Processing V", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "contributor": [ { "family_name": "Aldroubi", "given_name": "Akram", "clpid": "Aldroubi-A" }, { "family_name": "Laine", "given_name": "Andrew F.", "clpid": "Laine-A-F" }, { "family_name": "Unser", "given_name": "Michael A.", "clpid": "Unser-M-A" } ], "abstract": "The conditions for optimality of uniform orthonormal subband coders are reviewed. A number of properties of optimal filter banks are then summarized. The case of nonuniform orthonormal filter banks is also considered, and it is shown that the well known connection between optimal coding gain, energy compaction, and principle component property does not extend to the nonuniform case.", "doi": "10.1117/12.279683", "isbn": "9780819425911", "publisher": "Society of Photo-optical Instrumentation Engineers (SPIE)", "place_of_publication": "Bellingham, WA", "publication_date": "1997-10-30", "pages": "106-117" }, { "id": "authors:29jjh-ecf02", "collection": "authors", "collection_id": "29jjh-ecf02", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TUQiscassp97", "type": "book_section", "title": "Optimum low cost two channel IIR orthonormal filter bank", "book_title": "IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-97), Munich", "author": [ { "family_name": "Tuqan", "given_name": "Jamal", "clpid": "Tuqan-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "In this paper, we statistically optimize a well known class of IIR two channel orthonormal filter banks parameterized by a single coefficient when subband quantizers are present. The optimization procedure is extremely simple and very fast compared for example to the linear programming method used in the FIR case to achieve similar compaction (coding) gains. The special form of the filters assure the existence of a zero at \u03c0 which can be important for some wavelet applications and eliminate some of the major concerns that arise in the FIR design case. Finally, the compaction gain obtained is high and numerically very close to two (ideal case) for low pass spectra, high pass spectra and certain cases of multiband spectra. For these cases, the use of higher order IIR filters does not increase the compaction (coding) gain.", "doi": "10.1109/ICASSP.1997.599546", "isbn": "0818679190", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1997-04-01", "pages": "2425-2428" }, { "id": "authors:e78yh-kmt67", "collection": "authors", "collection_id": "e78yh-kmt67", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TUQasilo96", "type": "book_section", "title": "Optimum quantization of a class of non-bandlimited signals", "book_title": "Asilomar Conference on Signals, Systems and Computers, 30th, 1996", "author": [ { "family_name": "Tuqan", "given_name": "Jamal", "clpid": "Tuqan-J" }, { "family_name": "Vaidyanathan", "given_name": "P.P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We consider the quantization of a special class of non\nbandlimited signals, namely the class of discrete time signals that can be recovered from their decimated version. Similar to sigma-delta modulation ideas, we show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of these signals. We then consider noise shaping by optimizing a pre- and post filter around the quantizer and develop a closed form expression for the coding gain of the scheme under study. The use of\nan orthonormal filter bank as a sophisticated quantizer is\ninvestigated and several examples are provided.", "doi": "10.1109/ACSSC.1996.599181", "isbn": "0-8186-7646-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1996-11-01", "pages": "1396-1400" }, { "id": "authors:yt07q-ajk08", "collection": "authors", "collection_id": "yt07q-ajk08", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:TUQiscas96", "type": "book_section", "title": "Optimum pre- and postfilters for quantization", "book_title": "IEEE International Symposium on Circuits and Systems (ISCAS '96), 'Connecting the World', Atlanta, May 1996", "author": [ { "family_name": "Tuqan", "given_name": "Jamal", "clpid": "Tuqan-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We consider the optimization of pre- and post filters surrounding a uniform quantizer such that the mean square error due to quantization is minimized. Unlike some previous work, the postfilter is not restricted to be the inverse of the prefilter. With no order constraint on the filters, we present closed form solutions for the optimum pre- and post filters. Using these optimum solutions, we obtain a coding gain expression for the system under study. We then repeat the same analysis with first order pre- and post filters in the form 1+\u03b1z^-1 and 1/(1+\u03b3z^-1) providing some examples where we compare coding gain performance with the case of \u03b1=\u03b3.", "doi": "10.1109/ISCAS.1996.541746", "isbn": "0780330730", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1996-05-01", "pages": "461-464" }, { "id": "authors:qxzq1-29310", "collection": "authors", "collection_id": "qxzq1-29310", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150514-160507475", "type": "book_section", "title": "Considerations in the design of optimum compaction filters for subband coders", "book_title": "8th European Signal Processing Conference. EUSIPCO 1996", "author": [ { "family_name": "Lin", "given_name": "Yuan-Pei", "clpid": "Lin-Yuan-Pei" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Recently there has been considerable interest in the\ndesign of optimal paraunitary filter banks for a given\nclass of inputs. In this paper we address a number of\npractical considerations associated with the design and\nimplementation of optimal paraunitary filter banks.", "isbn": "978-888-6179-83-6", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1996" }, { "id": "authors:wam7g-jp227", "collection": "authors", "collection_id": "wam7g-jp227", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170606-155531191", "type": "book_section", "title": "Nonuniform decimation and reconstruction of generalized-bandlimited MD signals", "book_title": "1993 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Chen", "given_name": "Tsuhan", "clpid": "Chen-Tsuhan" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "It is well known that the data rate of bandlimited signals can be reduced without loss of information. One scheme which achieves this goal is the so-called nonuniform decimation. Recent results show that a bandlimited signal can be reconstructed from a nonuniformly decimated version. Theoretical results and efficient reconstruction methods have been addressed for one-dimensional signals. For the multidimensional case, some partial results are known. In this paper, we will discuss in detail the theory and implementation of the reconstruction of generalized-bandlimited multidimensional signals from their nonuniformly decimated versions.", "doi": "10.1109/ISCAS.1993.393672", "isbn": "0-7803-1281-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1993-05", "pages": "120-123" }, { "id": "authors:8es5j-yyr53", "collection": "authors", "collection_id": "8es5j-yyr53", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170606-153356272", "type": "book_section", "title": "Considerations in multidimensional filter bank design", "book_title": "1993 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Chen", "given_name": "Tsuhan", "clpid": "Chen-Tsuhan" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Onedimensional (1D) and multidimensional (MD) analysis/synthesis filter banks have attracted much attention recently. While 1D filer banks have been well studied and various design approaches have been successfully developed, many problems in the MD case remain unsolved. In this paper, we exploit a number of issues in MD filter bank design, including: the choice of permissible passband supports, the cyclic property of decimation matrices that is required for filter bank design using transformations, etc. We also propose a class of useful tree-structure filter banks, which apply to the commonly-used hexagonal decimation.", "doi": "10.1109/ISCAS.1993.393803", "isbn": "0-7803-1281-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1993-05", "pages": "643-646" }, { "id": "authors:20234-hs616", "collection": "authors", "collection_id": "20234-hs616", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170606-161238270", "type": "book_section", "title": "Biorthonormal filter banks: some necessary conditions, and orthonormalization", "book_title": "1993 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Djokovic", "given_name": "Igor", "clpid": "Djokovic-I" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "We first study some properties of nonuniform biorthonormal filter banks. We show that biorthonormality imposes a number of restrictions on the decimation ratios, e.g., they cannot be relatively prime. Also biorthonormality implies orthonormality when all the impulse responses have the same energy. After a brief study of these properties we show how to orthonormalize a nonuniform biorthonormal system by a procedure that is somewhat similar in spirit to (but fundamentally different from) the Gram Schmidt procedure. We then modify the procedure for the purpose of designing biort honormal filter banks that completely decorrelate the subband signals for a given input statistics.", "doi": "10.1109/ISCAS.1993.393808", "isbn": "0-7803-1281-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1993-05", "pages": "663-666" }, { "id": "authors:t8y75-d7m75", "collection": "authors", "collection_id": "t8y75-d7m75", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170606-151551464", "type": "book_section", "title": "Efficient subband encoding of magnitude/phase spectra", "book_title": "1993 IEEE International Symposium on Circuits and Systems", "author": [ { "family_name": "Soman", "given_name": "A. K.", "clpid": "Soman-A-K" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "For certain types of signals, perfect reconstruction is not essential. It is sufficient to have knowledge of either the magnitude or the phase spectrum only. Filter banks which introduce phase distortion are used for encoding speech signals. These schemes have an inherent redundancy; i.e., the samples are still transmitted at the sampling rate. It is shown how magnitude or phase information can be encoded at only half the sampling rate in a filter bank formalism.", "doi": "10.1109/ISCAS.1993.393739", "isbn": "0-7803-1281-3", "publisher": "IEEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1993-05", "pages": "387-390" }, { "id": "authors:ap0v6-5k207", "collection": "authors", "collection_id": "ap0v6-5k207", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170711-160844112", "type": "book_section", "title": "Theory and design of perfect reconstruction transmultiplexers and their relation to perfect reconstruction QMF banks", "author": [ { "family_name": "Koilpillai", "given_name": "R. D.", "clpid": "Koilpillai-R-D" }, { "family_name": "Nguyen", "given_name": "T. Q.", "clpid": "Nguyen-T-Q" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The theory of transmultiplexers involves the design of \nfilters for interconversion between Time Domain Multiplexing (TDM) and Frequency Division Multiplexing (FDM), such that the undesirable Crosstalk is minimized. \nIn TDM \u2192 FDM \u2192 TDM conversion, the perfect reconstruction \ntrans-multiplexer (PR-TMUX) achieves complete Crosstalk Cancellation (CC) and is distortion-free. In this \npaper, we present an analysis of the PR-TMUX based \non the polyphase component matrices of the filter banks used in TDM \u2192 FDM and FDM \u2192 TDM conversion respectively. Using that, a necessary and sufficient condition for \ncomplete CC is obtained. The close relation between \nPR-TMUX filters and PR-QMF banks is used to obtain \na direct design procedure for PR-TMUX filters.", "doi": "10.1109/ACSSC.1989.1200790", "publisher": "IEEE", "publication_date": "1989-10" }, { "id": "authors:yrk6z-4vc26", "collection": "authors", "collection_id": "yrk6z-4vc26", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170711-154504365", "type": "book_section", "title": "FIR and IIR techniques for bandlimited extrapolation of sequences", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Sath\u00e9", "given_name": "V. P.", "clpid": "Sath\u00e9-V-P" } ], "abstract": "The problem of extrapolating a finite length sequence into a band-limited sequence has been formulated in the past in terms of pseudoinverse techniques. Iterative and non-iterative algorithms for the extrapolation have also been proposed. All these algorithms, however, attempt to produce an ideally band-limited answer, which, in reality, is infinitely long and noncausal, and cannot be generated in finite time. In this paper the problem is converted to one of finding a finite length input to a practical FIR or IIR filter in such a way that a segment of the output matches the signal to be extrapolated. The fact that the generated signal is the output of a filter ensures that it is bandlimited to an extent determined largely by the filter quality. The advantage of this viewpoint is that we can exploit the rich literature which is available for efficient filter implementation (such as multistage and IFIR techniques, and efficient IIR techniques based on allpass building blocks).", "doi": "10.1109/ACSSC.1989.1200783", "publisher": "IEEE", "publication_date": "1989-10" }, { "id": "authors:jrqz6-1g402", "collection": "authors", "collection_id": "jrqz6-1g402", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120621-104329715", "type": "book_section", "title": "A new breakthrough in linear-system theory: Kharitonov's result", "book_title": "Twenty-Second Asolimar Conference on Signals, Systems and Computers", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Given a real coefficient polynomial D(s), there exist several procedures for testing whether it is strictly\nHurwitz (i.e., whether it has all its zeros in the open left-half plane). If the coefficients of D(s) are uncertain and belong to a known interval, such testing becomes more complicated because there is an infinitely large family of polynomials to which D(s) now belongs. It was shown by Kharitonov that in this case it is necessary and sufficient to test only four polynomials in order to know whether every polynomial in the family is strictly Hurwitz. An interpretation of this result in terms of reactance functions (i.e., LC impedances) was recently proposed. These results were also extended recently for the testing of positive real property of rational transfer functions with uncertain denominators. In this paper we review these results along with detailed proofs and discuss extensions to the discrete-time case.", "doi": "10.1109/ACSSC.1988.753943", "isbn": "0929029151", "publisher": "Maple Press", "place_of_publication": "San Jose, CA", "publication_date": "1988-10", "pages": "1-14" }, { "id": "authors:5p7kx-1n180", "collection": "authors", "collection_id": "5p7kx-1n180", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170713-131749478", "type": "book_section", "title": "Roundoff noise generated by orthogonal building blocks in signal processing structures", "author": [ { "family_name": "Liu", "given_name": "Vincent C.", "clpid": "Liu-Vincent-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The statistics of roundoff errors produced by the multiplication of a random input vector with an orthogonal matrix can be expressed in terms of the characteristic function of the input vector. The case of a 2*2 orthogonal matrix is analyzed by assuming that the input probability mass function follows a jointly Gaussian envelope. It is found that for small dynamic ranges the two errors are not necessarily uncorrelated. However, they are uncorrelated for large dynamic range. The lossless FIR (finite-impulse-response) lattice with quantizers is considered as an example.", "doi": "10.1109/ISCAS.1988.15504", "publisher": "IEEE", "publication_date": "1988-06" }, { "id": "authors:yp4cy-cxh21", "collection": "authors", "collection_id": "yp4cy-cxh21", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-173931829", "type": "book_section", "title": "Perfect reconstruction QMF structures which yield linear phase FIR analysis filters", "author": [ { "family_name": "Nguyen", "given_name": "T. Q.", "clpid": "Nguyen-T-Q" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "The authors present a perfect reconstruction FIR (finite-impulse response) linear-phase lattice structure for the two-channel quadrature-mirror-filter (QMF) bank. This structure covers most pairs of perfect reconstruction FIR linear-phase analysis filters which have the same (odd) order. For general number of channels M, conditions are derived which any QMF perfect reconstruction linear phase structure must obey. A design example is presented for the M=2 case.", "doi": "10.1109/ISCAS.1988.14925", "publisher": "IEEE", "publication_date": "1988-06" }, { "id": "authors:yf740-28033", "collection": "authors", "collection_id": "yf740-28033", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-171715402", "type": "book_section", "title": "A tutorial on multirate digital filter banks", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "A number of topics in multirate digital signal processing, such as decimation and interpolation, polyphase structures, power-complementary and Mth band filters, and digital filter banks are reviewed. Maximally decimated digital filter banks are emphasized, and the problem of perfect reconstruction reviewed. The role of FIR (finite-impulse-response) lossless systems in this context is also reviewed.", "doi": "10.1109/ISCAS.1988.15391", "publisher": "IEEE", "publication_date": "1988-06" }, { "id": "authors:6xa34-w4q30", "collection": "authors", "collection_id": "6xa34-w4q30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170713-131323534", "type": "book_section", "title": "Eigenfilters for the design of special transfer functions with applications in multirate signal processing", "author": [ { "family_name": "Nguyen", "given_name": "T. Q.", "clpid": "Nguyen-Truong-Q" }, { "family_name": "Saramaki", "given_name": "T.", "clpid": "Saramaki-T" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "Based on the multistage approach, a design procedure is presented for finding a spectral factor of an mth-band filter and for designing multistage decimation filters. The proposed design method finds spectral factors of mth-band FIR (finite-impulse response) filters without direct computation, and yields filters with much higher attenuation than would be possible by conventional methods. Such mth-band filters are used in filter-bank designs, including perfect-reconstruction systems.", "doi": "10.1109/ICASSP.1988.196878", "publisher": "IEEE", "publication_date": "1988-04" }, { "id": "authors:s8ye2-sq602", "collection": "authors", "collection_id": "s8ye2-sq602", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-172701882", "type": "book_section", "title": "Improved approach for design of perfect reconstruction FIR QMF banks, with lossless lattice structures", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Nguyen", "given_name": "T. Q.", "clpid": "Nguyen-T-Q" }, { "family_name": "Saramaki", "given_name": "T.", "clpid": "Saramaki-T" } ], "abstract": "A property of FIR (finite-impulse response) lossless systems is introduced, leading to substantial improvement in the sign procedure for perfect-reconstruction QMF (quadrature mirror filter) banks. The property enables the designer to initialize the coefficients of a lattice structure (which characterizes the analysis bank), in such a way as to speed up to the convergence. A design example is provided. Compared to other methods, the proposed method is shown to converge faster, and always leads to much improved attenuation characteristics for a given filter length.", "doi": "10.1109/ICASSP.1988.196879", "publisher": "IEEE", "publication_date": "1988-04" }, { "id": "authors:0mefx-ab702", "collection": "authors", "collection_id": "0mefx-ab702", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170718-162454239", "type": "book_section", "title": "The perfect-reconstruction QMF bank: New architectures, solutions, and optimization strategies", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Hoang", "given_name": "Phuong-Quan", "clpid": "Hoang-Phuong-Quan" } ], "abstract": "n this paper, a scheme for perfect reconstruction in M channel, maximally decimated QMF banks is first presented, for arbitrary M. The solutions are such that the analysis and synthesis filters are FIR and of the same length. Based on the theory, lattice structures for the two-channel case are derived, which offer an efficient design as well as implementation procedure for two-channel perfect reconstruction systems. Such lattice implementations are robust in the sense that the perfect-reconstruction property is preserved in spite of coefficient quantization.", "doi": "10.1109/ICASSP.1987.1169403", "publisher": "IEEE", "publication_date": "1987-04" }, { "id": "authors:4xaxn-kqk60", "collection": "authors", "collection_id": "4xaxn-kqk60", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170718-174605100", "type": "book_section", "title": "Design of doubly-complementary IIR digital filters, using a single complex allpass filter", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Regalia", "given_name": "P.", "clpid": "Regalia-P" }, { "family_name": "Mitra", "given_name": "S. K.", "clpid": "Mitra-S-K" } ], "abstract": "It is shown that a wide class of real-coefficient, doubly-complementary IIR transfer-function pairs can be implemented by means of a single complex allpass filter. For a real input sequence, the real part of the output sequence of the complex allpass filter corresponds to one of the transfer functions G(z) (for example, low-pass), whereas the imaginary part of the output sequence corresponds to its \"complementary\" filter H(z) (for example, highpass). Since the resulting implementation is structurally lossless, G(z) and H(z) have very low passband-sensitivity. Numerical design examples are included to demonstrate the ideas.", "doi": "10.1109/ICASSP.1986.1169285", "publisher": "IEEE", "publication_date": "1986-04" }, { "id": "authors:e9exp-sx278", "collection": "authors", "collection_id": "e9exp-sx278", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170718-174241392", "type": "book_section", "title": "New cascaded lattice structures for FIR filters having extremely low coefficent sensitivity", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "It is shown that any arbitrary FIR transfer function can be implemented in the form of a passive structure, resulting in low coefficient sensitivity. The building blocks are planar-rotation operators, and internal signal nodes are automatically L_2-scaled. Denormalized versions of the building blocks are also shown. Design examples are included.", "doi": "10.1109/ICASSP.1986.1169027", "publisher": "IEEE", "publication_date": "1986-04" }, { "id": "authors:vh3hh-ybx44", "collection": "authors", "collection_id": "vh3hh-ybx44", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170725-171143824", "type": "book_section", "title": "New design methods for FIR filters with equiripple stopbands and prescribed degrees of passband flatness", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "abstract": "A technique is presented for designing linear-phase digital FIR filters, with a prescribed degree of flatness in the passband, and a prescribed (equiripple) attenuation in the stopband. The design is based entirely on appropriate use of the McClellan-Parks algorithm along with certain maximally flat building blocks.", "doi": "10.1109/ICASSP.1985.1168460", "publisher": "IEEE", "publication_date": "1985-04" }, { "id": "authors:v9e1d-66r22", "collection": "authors", "collection_id": "v9e1d-66r22", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170727-154940505", "type": "book_section", "title": "A new class of very low sensitivity cascade-form digital-filters based on \"passive\" second order single-input single-output building blocks", "author": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Mitra", "given_name": "S. K.", "clpid": "Mitra-S-K" } ], "abstract": "A new type of cascade form structure for digital filtering is proposed, with each building block being a second order section, that satisfies certain passivity properties. This passivity is essentially a \"structure-induced\" boundedness on the transfer function magnitude, and leads to low passband sensitivity. In addition, the cascade nature ensures low stopband sensitivity, as zeros on the unit circle continue to remain on the unit circle in spite of the quantization. The structure itself is independent of the pole locations and therefore meets a wide range of filtering applications.", "doi": "10.1109/ICASSP.1984.1172364", "publisher": "IEEE", "publication_date": "1984-03" } ]