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
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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