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Iterative greedy algorithm for solving the FIR paraunitary approximation problem

Tkacenko, Andre and Vaidyanathan, P. P. (2006) Iterative greedy algorithm for solving the FIR paraunitary approximation problem. IEEE Transactions on Signal Processing, 54 (1). pp. 146-160. ISSN 1053-587X. https://resolver.caltech.edu/CaltechAUTHORS:TKAieeetsp06a

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Abstract

In this paper, a method for approximating a multi-input multi-output (MIMO) transfer function by a causal finite-impulse response (FIR) paraunitary (PU) system in a weighted least-squares sense is presented. Using a complete parameterization of FIR PU systems in terms of Householder-like building blocks, an iterative algorithm is proposed that is greedy in the sense that the observed mean-squared error at each iteration is guaranteed to not increase. For certain design problems in which there is a phase-type ambiguity in the desired response, which is formally defined in the paper, a phase feedback modification is proposed in which the phase of the FIR approximant is fed back to the desired response. With this modification in effect, it is shown that the resulting iterative algorithm not only still remains greedy, but also offers a better magnitude-type fit to the desired response. Simulation results show the usefulness and versatility of the proposed algorithm with respect to the design of principal component filter bank (PCFB)-like filter banks and the FIR PU interpolation problem. Concerning the PCFB design problem, it is shown that as the McMillan degree of the FIR PU approximant increases, the resulting filter bank behaves more and more like the infinite-order PCFB, consistent with intuition. In particular, this PCFB-like behavior is shown in terms of filter response shape, multiresolution, coding gain, noise reduction with zeroth-order Wiener filtering in the subbands, and power minimization for discrete multitone (DMT)-type transmultiplexers.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TSP.2005.861054DOIUNSPECIFIED
ORCID:
AuthorORCID
Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© Copyright 2006 IEEE. Reprinted with permission. Manuscript received February 21, 2004; revised January 25, 2005. [Posted online: 2005-12-19] This work was supported in part by the NSF grant CCF-0428326, ONR grant N00014-06-1-0011, and the California Institute of Technology. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Henrique Malvar.
Subject Keywords:Filter bank optimization, greedy algorithm, interpolation, principal components filter bank
Issue or Number:1
Record Number:CaltechAUTHORS:TKAieeetsp06a
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:TKAieeetsp06a
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6402
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:07 Dec 2006
Last Modified:09 Mar 2020 13:19

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