Performance analysis and optimal filter design for sigma-delta modulation via duality with DPCM

Or Ordentlich, Uri Erez

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Sampling above the Nyquist rate is at the heart of sigma-delta modulation, where the increase in sampling rate is translated to a reduction in the overall (mean-squared-error) reconstruction distortion. This is attained by using a feedback filter at the encoder, in conjunction with a low-pass filter at the decoder. The goal of this paper is to characterize the optimal trade-off between the per-sample quantization rate and the resulting mean-squared-error distortion under various restrictions on the feedback filter. To this end, we establish a duality relation between the performance of sigma-delta modulation and the performance of differential pulse-code modulation when applied to (discrete-time) band-limited inputs. As the optimal trade-off for the latter scheme is fully understood, the full characterization for sigma-delta modulation, as well as the optimal feedback filters, immediately follows.

Original languageAmerican English
Article number8537788
Pages (from-to)1153-1164
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number2
StatePublished - Feb 2019

Bibliographical note

Publisher Copyright:
© 2018 IEEE.


  • Quantization
  • analog-to-digital conversion
  • differential pulse-code modulation
  • sigma-delta modulation


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