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Classical sampling theorems in the context of multirate and polyphase digital filter bank structures

Vaidyanathan, P. P. and Liu, Vincent C. (1988) Classical sampling theorems in the context of multirate and polyphase digital filter bank structures. IEEE Transactions on Acoustics, Speech, and Signal Processing, 36 (9). pp. 1480-1495. ISSN 0096-3518. http://resolver.caltech.edu/CaltechAUTHORS:VAIieeetassp88a

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Abstract

The recovery of a signal from so-called generalized samples is a problem of designing appropriate linear filters called reconstruction (or synthesis) filters. This relationship is reviewed and explored. Novel theorems for the subsampling of sequences are derived by direct use of the digital-filter-bank framework. These results are related to the theory of perfect reconstruction in maximally decimated digital-filter-bank systems. One of the theorems pertains to the subsampling of a sequence and its first few differences and its subsequent stable reconstruction at finite cost with no error. The reconstruction filters turn out to be multiplierless and of the FIR (finite impulse response) type. These ideas are extended to the case of two-dimensional signals by use of a Kronecker formalism. The subsampling of bandlimited sequences is also considered. A sequence x(n ) with a Fourier transform vanishes for |ω|&ges;Lπ/M, where L and M are integers with L<M, can in principle be represented by reducing the data rate by the amount M/L. The digital polyphase framework is used as a convenient tool for the derivation as well as mechanization of the sampling theorems


Item Type:Article
Additional Information:© Copyright 1988 IEEE. Reprinted with permission. Manuscript received October 13, 1987; revised March 5, 1988. This work was supported in part by the National Science Foundation under Grant DCI 8552579, by the matching funds provided by Pacific Bell and General Electric Co., by Caltech’s Programs in Advanced Technology grant sponsored by Aerojet General, General Motors, GTE, and TRW, and by the National Science Foundation under Grant MIP 8604456.
Subject Keywords:Fourier transforms; computerised signal processing; digital filters; filtering and prediction theory
Record Number:CaltechAUTHORS:VAIieeetassp88a
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:VAIieeetassp88a
Alternative URL:http://dx.doi.org/10.1109/29.90376
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5464
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:18 Oct 2006
Last Modified:26 Dec 2012 09:12

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