Distortion rate function of sub-Nyquist sampled Gaussian sources corrupted by noise

Alon Kipnis, Andrea J. Goldsmith, Tsachy Weissman, Yonina C. Eldar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

The amount of information lost in sub-Nyquist uniform sampling of a continuous-time Gaussian stationary process is quantified. We first derive an expression for the mean square error in reconstruction of the process for a given sampling structure as a function of the sampling frequency and the average number of bits describing each sample. We define this function as the distortion-rate-frequency function. It is obtained by reverse water-filling over spectral density associated with the minimum variance reconstruction of an undersampled Gaussian process, plus the error in this reconstruction. Further optimization is then performed over the sampling structure, and an optimal pre-sampling filter associated with the statistic of the input signal and the sampling frequency is found. This results in an expression for the minimal possible distortion achievable under any uniform sampling scheme. This expression is calculated for several examples to illustrate the fundamental tradeoff between rate distortion and sampling frequency derived in this work that lies at the intersection of information theory and signal processing.

Original languageEnglish (US)
Title of host publication2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013
PublisherIEEE Computer Society
Pages901-908
Number of pages8
ISBN (Print)9781479934096
DOIs
StatePublished - 2013
Externally publishedYes
Event51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013 - Monticello, IL, United States
Duration: Oct 2 2013Oct 4 2013

Publication series

Name2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013

Other

Other51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013
CountryUnited States
CityMonticello, IL
Period10/2/1310/4/13

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Control and Systems Engineering

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