Oversampling PCM Techniques and Optimum Noise Shapers for Quantizing a Class of Nonbandlimited Signals,
Abstract
We consider the quantization of a class of non bandlimited signals, namely the class of discrete time signals that can be recovered from their decimated version. Based on recent results, the signals of interest are assumed to be the output of a single interpolation filter (single band model) or more generally the. sum of the outputs of L interpolation filters (multiband model). By definition, these signals are oversampled and it is reasonable to expect that we can reap the same benefits of well known efficient A/D techniques. In fact, by using appropriate multirate models and reconstruction schemes, we first show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of the signals. Alternatively, we also show that 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 pre and post filters around the quantizer. We start with a scalar time invariant quantizer and study two important cases of LTI filters, namely the case where the postfilter is the inverse of the prefilter and the more general case where the postfilter is not related to the prefilter. Closed form expressions for the optimum filters and minimum mean squared error are derived in each case for both the single band and multiband models. Due to the statistical nature of the signal of interest, 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. Because the general (LPTV)M case is difficult to track analytically, we study two special cases in great detail and give complete solutions for both the single band and multiband models.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1996
- Accession Number
- ADA323685
Entities
People
- Jamal Tuqan
- Palghat Vaidyanathan
Organizations
- California Institute of Technology