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A Deterministic Analysis of Decimation for Sigma-Delta Quantization of Bandlimited Functions

Publication ,  Journal Article
Daubechies, I; Saab, R
Published in: IEEE Signal Processing Letters
November 1, 2015

We study Sigma-Delta (Σ Δ) quantization of oversampled bandlimited functions. We prove that digitally integrating blocks of bits and then down-sampling, a process known as decimation, can efficiently encode the associated Σ Δ bit-stream. It allows a large reduction in the bit-rate while still permitting good approximation of the underlying bandlimited function via an appropriate reconstruction kernel. Specifically, in the case of stable rth order Σ Δ schemes we show that the reconstruction error decays exponentially in the bit-rate. For example, this result applies to the 1-bit, greedy, first-order Σ Δ scheme.

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Published In

IEEE Signal Processing Letters

DOI

ISSN

1070-9908

Publication Date

November 1, 2015

Volume

22

Issue

11

Start / End Page

2093 / 2096

Related Subject Headings

  • Networking & Telecommunications
  • 4603 Computer vision and multimedia computation
  • 4009 Electronics, sensors and digital hardware
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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Daubechies, I., & Saab, R. (2015). A Deterministic Analysis of Decimation for Sigma-Delta Quantization of Bandlimited Functions. IEEE Signal Processing Letters, 22(11), 2093–2096. https://doi.org/10.1109/LSP.2015.2459758
Daubechies, I., and R. Saab. “A Deterministic Analysis of Decimation for Sigma-Delta Quantization of Bandlimited Functions.” IEEE Signal Processing Letters 22, no. 11 (November 1, 2015): 2093–96. https://doi.org/10.1109/LSP.2015.2459758.
Daubechies I, Saab R. A Deterministic Analysis of Decimation for Sigma-Delta Quantization of Bandlimited Functions. IEEE Signal Processing Letters. 2015 Nov 1;22(11):2093–6.
Daubechies, I., and R. Saab. “A Deterministic Analysis of Decimation for Sigma-Delta Quantization of Bandlimited Functions.” IEEE Signal Processing Letters, vol. 22, no. 11, Nov. 2015, pp. 2093–96. Scopus, doi:10.1109/LSP.2015.2459758.
Daubechies I, Saab R. A Deterministic Analysis of Decimation for Sigma-Delta Quantization of Bandlimited Functions. IEEE Signal Processing Letters. 2015 Nov 1;22(11):2093–2096.

Published In

IEEE Signal Processing Letters

DOI

ISSN

1070-9908

Publication Date

November 1, 2015

Volume

22

Issue

11

Start / End Page

2093 / 2096

Related Subject Headings

  • Networking & Telecommunications
  • 4603 Computer vision and multimedia computation
  • 4009 Electronics, sensors and digital hardware
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing