Optimal trade-off between sampling rate and quantization precision in Sigma-Delta A/D conversion

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

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

7 Scopus citations

Abstract

The optimal sampling frequency in a Sigma-Delta analog-to-digital converter with a fixed bitrate at the output is studied. We consider the mean squared error performance metric where the input signal statistics are known. Fixing the output bitrate introduces a trade-off between the sampling rate and the number of bits used to quantize each sample. That is, while increasing the sampling rate reduces the in-band quantization noise, it also reduces the number of bits available to quantize each sample and therefore increases the magnitude of the quantization noise. The optimal sampling rate is the result of the interplay between these two phenomena. In this work we analyze the sampling rate of a Sigma-Delta modulator of arbitrary order under the approximation that the quantization error behaves like additive white noise that is uncorrelated with the signal. We show that for a signal with a spectrum that is constant over its bandwidth, the optimal sampling rate is either the Nyquist rate or the maximal sampling rate corresponding to the output bitrate. The choice between the two is approximately a function of the Sigma-Delta system order and the bitrate per unit bandwidth.

Original languageEnglish (US)
Title of host publication2015 International Conference on Sampling Theory and Applications, SampTA 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages627-631
Number of pages5
ISBN (Electronic)9781467373531
DOIs
StatePublished - Jul 2 2015
Externally publishedYes
Event11th International Conference on Sampling Theory and Applications, SampTA 2015 - Washington, United States
Duration: May 25 2015May 29 2015

Publication series

Name2015 International Conference on Sampling Theory and Applications, SampTA 2015

Conference

Conference11th International Conference on Sampling Theory and Applications, SampTA 2015
Country/TerritoryUnited States
CityWashington
Period5/25/155/29/15

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Signal Processing
  • Statistics and Probability

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