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A state space approach to the design of globally optimal FIR energy compaction filters

Tuqan, Jamal and Vaidyanathan, P. P. (2000) A state space approach to the design of globally optimal FIR energy compaction filters. IEEE Transactions on Signal Processing, 48 (10). pp. 2822-2838. ISSN 1053-587X. http://resolver.caltech.edu/CaltechAUTHORS:TUQieeetsp00

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Abstract

We introduce a new approach for the least squared optimization of a weighted FIR filter of arbitrary order N under the constraint that its magnitude squared response be Nyquist(M). Although the new formulation is general enough to cover a wide variety of applications, the focus of the paper is on optimal energy compaction filters. The optimization of such filters has received considerable attention in the past due to the fact that they are the main building blocks in the design of principal component filter banks (PCFBs). The newly proposed method finds the optimum product filter Fopt(z)=Hopt(Z)Hopt (z^-1) corresponding to the compaction filter Hopt (z). By expressing F(z) in the form D(z)+D(z^-1), we show that the compaction problem can be completely parameterized in terms of the state-space realization of the causal function D(z). For a given input power spectrum, the resulting filter Fopt(z) is guaranteed to be a global optimum solution due to the convexity of the new formulation. The new algorithm is universal in the sense that it works for any M, arbitrary filter length N, and any given input power spectrum. Furthermore, additional linear constraints such as wavelets regularity constraints can be incorporated into the design problem. Finally, obtaining Hopt(z) from Fopt(z) does not require an additional spectral factorization step. The minimum-phase spectral factor Hmin(z) can be obtained automatically by relating the state space realization of Dopt(z) to that of H opt(z)


Item Type:Article
Additional Information:© Copyright 2000 IEEE. Reprinted with permission. Manuscript received August 9, 1999; revised May 12, 2000. This work was supported in part by the National Science Foundation under Grant 0703755. The associate editor coordinating the review of this paper and approving it for publication was Prof. Hideaki Sakai. The authors would like to thank Prof. S. Boyd (Stanford University) and Prof. L. Vandenberghe (UCLA) for generously making available their SDP software which was used to validate earlier versions of our results. They would also like to thank Prof. M. G. Strintzis for sending a preprint of [21].
Subject Keywords:Discrete-time positive real lemma, energy compaction filters, Kalman–Yakubovich–Popov (KYP) lemma, linear matrix inequality (LMI), optimum orthonormal subband coder (SBC), principal components filter bank (PCFB), semi-definite programming (SDP)
Record Number:CaltechAUTHORS:TUQieeetsp00
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:TUQieeetsp00
Alternative URL:http://dx.doi.org/10.1109/78.869032
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5381
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:16 Oct 2006
Last Modified:26 Dec 2012 09:05

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