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Eigenstructure Approach for Characterization of FIR PR Filterbanks With Order One Polyphase

Muthuvel, Arigovindan and Makur, Anamitra (2001) Eigenstructure Approach for Characterization of FIR PR Filterbanks With Order One Polyphase. In: IEEE Transactions on Signal Processing, 49 (10). pp. 2283-2291.

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Abstract

In this paper, a new approach for the characterization of M-channel finite impulse response (FIR) perfect reconstruction (PR) filterbanks is proposed. By appropriately restricting the eigenstructure of the polyphase matrix of the bank, a complete characterization of order-one polyphase matrices is obtained in which the polynomial part is in a block diagonal form. Nilpotent matrices play a crucial role in the structure. This structure allows imposing restrictions on the order of the inverse of the polyphase matrix and/or analysis-synthesis delay (reconstruction delay). Next, we derive an alternate complete characterization in terms of the degree of the determinant and the McMillan degree of order-one polyphase matrix, which we call the dyadic-based characterization. The characterization of Vaidyanathan and Chen for matrices with anticausal inverse turns out to be a special case of the proposed characterization. The dyadic-based characterization is more suitable for design without any above-mentioned restriction since it allows better initialization. We finally present design examples with different cost functions.

Item Type: Journal Article
Additional Information: 2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE
Keywords: Eigenstructure;FIR filterbank;McMillan degree;Nilpotent matrix
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 22 Aug 2008
Last Modified: 01 Jul 2011 09:06
URI: http://eprints.iisc.ernet.in/id/eprint/1964

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