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Linear phase paraunitary filter banks: theory, factorizations and designs

Soman, Anand K. and Vaidyanathan, P. P. and Nguyen, Truong Q. (1993) Linear phase paraunitary filter banks: theory, factorizations and designs. IEEE Transactions on Signal Processing, 41 (12). pp. 3480-3496. ISSN 1053-587X. http://resolver.caltech.edu/CaltechAUTHORS:SOMieeetsp93c

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Abstract

M channel maximally decimated filter banks have been used in the past to decompose signals into subbands. The theory of perfect-reconstruction filter banks has also been studied extensively. Nonparaunitary systems with linear phase filters have also been designed. In this paper, we study paraunitary systems in which each individual filter in the analysis synthesis banks has linear phase. Specific instances of this problem have been addressed by other authors, and linear phase paraunitary systems have been shown to exist. This property is often desirable for several applications, particularly in image processing. We begin by answering several theoretical questions pertaining to linear phase paraunitary systems. Next, we develop a minimal factorizdion for a large class of such systems. This factorization will be proved to be complete for even M. Further, we structurally impose the additional condition that the filters satisfy pairwise mirror-image symmetry in the frequency domain. This significantly reduces the number of parameters to be optimized in the design process. We then demonstrate the use of these filter banks in the generation of M-band orthonormal wavelets. Several design examples are also given to validate the theory.


Item Type:Article
Additional Information:© Copyright 1993 IEEE. Reprinted with permission. Manuscript received May 17, 1992; revised June 10, 1993. The Guest Editor coordinating the review of this paper and approving it for publication was Dr. Ahmed Tewfik. This was supported in part by the National Science Foundation under Grant MIP 8919196, in part by Tektronix Inc., and in part by Rockwell International.
Subject Keywords:digital filters, filtering and prediction theory, image processing, linear network analysis, linear network synthesis, wavelet transforms
Record Number:CaltechAUTHORS:SOMieeetsp93c
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:SOMieeetsp93c
Alternative URL:http://dx.doi.org/10.1109/78.258087
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8716
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:10 Sep 2007
Last Modified:26 Dec 2012 09:41

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