Principal component filter banks for optimal multiresolution analysis

Tsatsanis, M.K.; Giannakis, Georgios B.

doi:10.1109/78.403336

Cited by 172 publications

(145 citation statements)

References 22 publications

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“…Works in FIR perfect reconstruction filter bank design have largely focused on constructive methods using classic mean-square or least-squares approximation theory with constraints [3][4][5][6]. Realizations of paraunitary systems have largely been parametric or intrinsic parametrizations that employ lattice parameterizations in a linear or tree-based structure [7,[10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…They are useful for designing perfect-reconstruction filter banks in coding and image processing tasks [1][2][3][4][5][6][7] as well as for determining the eigenstructure of multichannel time series in direction-of-arrival estimation and wideband array processing tasks [8][9][10][11][12]. When m = n = 1, (4) guarantees that the single-input, single-output linear system W [z] is an all-pass filter, and thus solutions to (1)-(4) are useful for single-channel deconvolution, equalization, and adaptive control tasks [13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Gradient Adaptive Paraunitary Filter Banks for Spatio-Temporal Subspace Analysis and Multichannel Blind Deconvolution

Douglas

Амари

Kung

2004

The Journal of VLSI Signal Processing-Systems for Signal, Image

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Abstract. Paraunitary filter banks are important for several signal processing tasks, including coding, multichannel deconvolution and equalization, adaptive beamforming, and subspace processing. In this paper, we consider the task of adapting the impulse response of a multichannel paraunitary filter bank via gradient ascent or descent on a chosen cost function. Our methods are spatio-temporal generalizations of gradient techniques on the Grassmann and Stiefel manifolds, and we prove that they inherently maintain the paraunitariness of the multichannel adaptive system over time. We then discuss the necessary practical approximations, modifications, and simplifications of the methods for solving two relevant signal processing tasks: (i) spatio-temporal subspace analysis and (ii) multichannel blind deconvolution. Simulations indicate that our methods can provide simple, useful solutions to these important problems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gradient Adaptive Paraunitary Filter Banks for Spatio-Temporal Subspace Analysis and Multichannel Blind Deconvolution

Douglas

Амари

Kung

2004

The Journal of VLSI Signal Processing-Systems for Signal, Image

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“…1(b), then an optimal set of synthesis filters Fig. 1(a) which maximize σ 2 w from (6) are the first L ideal compaction filters appearing in the infinite order PCFB for Sxx(z) [5,8].…”

Section: Derivation Of the Energy Compaction Problemmentioning

confidence: 99%

“…The problem of the design of optimal signal-adapted multirate filter banks has been of interest to the signal processing community on account of its applications in signal representation and data compression [5,1,8]. Such filter banks are typically chosen to optimize a particular objective, such as coding gain or a multiresolution criterion, adapted to the input signal statistics.…”

Section: Introductionmentioning

confidence: 99%

“…Such filter banks are typically chosen to optimize a particular objective, such as coding gain or a multiresolution criterion, adapted to the input signal statistics. If no constraints are imposed on the orders of the analysis/synthesis filters, then the optimal filter bank for a number of objectives is an infinite order principal component filter bank (PCFB) [5,1]. Such a filter bank is simultaneously optimal for a wide variety of objectives, including those mentioned above.…”

Section: Introductionmentioning

confidence: 99%

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iterative eigenfilter method for designing optimum overdecimated orthonormal FIR compaction filter banks

Tkacenko

Vaidyanathan

The Thrity-Seventh Asilomar Conference on Signals, Systems &Amp; Computers, 2003

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Much attention has recently been given to the construction of signaladapted 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. 1

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Wavelets: A Multiscale Analysis Tool

Krim

2003

Wiley Encyclopedia of Telecommunications

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As a new analysis tool, the wavelet transform has had a profound impact on almost all disciplines requiring signal analysis of any significance. It provided for the first time a systematic scale‐based analysis, in contrast to filters, a tractable methodology in the temporal/spatial domain. Our goal, here, is to provide an introduction to this tool with an emphasis on gaining a working knowledge for an advanced undergraduate student. We highlight the merits of the tool as well as its limitations, and present it as complementary to the Fourier analysis tool, rather than as a universal panacea.

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Principal component filter banks for optimal multiresolution analysis

Cited by 172 publications

References 22 publications

Gradient Adaptive Paraunitary Filter Banks for Spatio-Temporal Subspace Analysis and Multichannel Blind Deconvolution

Gradient Adaptive Paraunitary Filter Banks for Spatio-Temporal Subspace Analysis and Multichannel Blind Deconvolution

iterative eigenfilter method for designing optimum overdecimated orthonormal FIR compaction filter banks

Wavelets: A Multiscale Analysis Tool

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