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Theory and design of uniform DFT, parallel, quadrature mirror filter banks

Swaminathan, Kumar and Vaidyanathan, P. P. (1986) Theory and design of uniform DFT, parallel, quadrature mirror filter banks. IEEE Transactions on Circuits and Systems, 33 (12). pp. 1170-1191. ISSN 0098-4094.

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In this paper, the theory of uniform DFT, parallel, quadrature mirror filter (QMF) banks is developed. The QMF equations, i.e., equations that need to be satisfied for exact reconstruction of the input signal, are derived. The concept of decimated filters is introduced, and structures for both analysis and synthesis banks are derived using this concept. The QMF equations, as well as closed-form expressions for the synthesis filters needed for exact reconstruction of the input signalx(n), are also derived using this concept. In general, the reconstructed. signalhat{x}(n)suffers from three errors: aliasing, amplitude distortion, and phase distortion. Conditions for exact reconstruction (i.e., all three distortions are zero, andhat{x}(n)is equal to a delayed version ofx(n))of the input signal are derived in terms of the decimated filters. Aliasing distortion can always be completely canceled. Once aliasing is canceled, it is possible to completely eliminate amplitude distortion (if suitable IIR filters are employed) and completely eliminate phase distortion (if suitable FIR filters are employed). However, complete elimination of all three errors is possible only with some simple, pathalogical stable filter transfer functions. In general, once aliasing is canceled, the other distortions can be minimized rather than completely eliminated. Algorithms for this are presented. The properties of FIR filter banks are then investigated. Several aspects of IIR filter banks are also studied using the same framework.

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Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© Copyright 1986 IEEE. Reprinted with permission. Manuscript received July 19, 1985; revised February 21, 1986. This work was supported in part by the National Science Foundation under Grant ECS 84-04245, and in part by CALTECH’s Program in Advanced Technology, sponsored by Aerojet General, General Motors, GTE, and TRW. This work was performed when the first author was with the California Institute of Technology.
Issue or Number:12
Record Number:CaltechAUTHORS:SWAieeetcs86
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6844
Deposited By: Archive Administrator
Deposited On:26 Dec 2006
Last Modified:09 Mar 2020 13:19

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