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Oversampling PCM techniques and optimum noise shapers for quantizing a class of nonbandlimited signals

Tuqan, Jamal and Vaidyanathan, P. P. (1999) Oversampling PCM techniques and optimum noise shapers for quantizing a class of nonbandlimited signals. IEEE Transactions on Signal Processing, 47 (2). pp. 389-407. ISSN 1053-587X. http://resolver.caltech.edu/CaltechAUTHORS:TUQieeetsp99

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Abstract

We consider the efficient quantization of a class of nonbandlimited signals, namely, the class of discrete-time signals that can be recovered from their decimated version. The signals are modeled as the output of a single FIR interpolation filter (single band model) or, more generally, as the sum of the outputs of L FIR interpolation filters (multiband model). These nonbandlimited signals are oversampled, and it is therefore reasonable to expect that we can reap the same benefits of well-known efficient A/D techniques that apply only to bandlimited signals. We first show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of the signals. We can achieve a substantial decrease in bit rate by appropriately decimating the signals and then quantizing them. To further increase the effective quantizer resolution, noise shaping is introduced by optimizing prefilters and postfilters around the quantizer. We start with a scalar time-invariant quantizer and study two important cases of linear time invariant (LTI) filters, namely, the case where the postfilter is the inverse of the prefilter and the more general case where the postfilter is independent from the prefilter. Closed form expressions for the optimum filters and average minimum mean square error are derived in each case for both the single band and multiband models. The class of noise shaping filters and quantizers is then enlarged to include linear periodically time varying (LPTV)M filters and periodically time-varying quantizers of period M. We study two special cases in great detail.


Item Type:Article
Additional Information:© Copyright 1999 IEEE Manuscript received December 19, 1996; revised July 31, 1998. This work was supported in part by the Office of Naval Research under Grant N00014-93-1-0231, Tektronix, Inc., and Rockwell International. The associate editor coordinating the review of this paper and approving it for publication was Dr. Troung Q. Nguyen.
Subject Keywords:Multirate signal processing, noise shaping, oversampling, PCM techniques, sampling theory
Record Number:CaltechAUTHORS:TUQieeetsp99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:TUQieeetsp99
Alternative URL:http://dx.doi.org/10.1109/78.740124
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4935
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:13 Sep 2006
Last Modified:26 Dec 2012 09:02

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