Towards a Better Understanding of 1-Bit Sigma-Delta Modulators - Part 3

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J. Vanderkooy, and ST. P.. Lipshitz, "Towards a Better Understanding of 1-Bit Sigma-Delta Modulators - Part 3," Paper 5620, (2002 April.). doi:
J. Vanderkooy, and ST. P.. Lipshitz, "Towards a Better Understanding of 1-Bit Sigma-Delta Modulators - Part 3," Paper 5620, (2002 April.). doi:
Abstract: This is Part 3 of our ongoing investigation into the behaviour of 1-bit sigma-delta modulators. It addresses the following topics: (a) Angus has claimed that an undithered 1-bit sigma-delta modulator is effectively self-dithered by its internal noise. We show that his conclusion is essentially a quasi-dc one, and that his pictures of self-dither, although suggestive, do not in fact signify the elimination of all correlated artefacts in the way achieved by a properly-dithered multi-bit modulator. (b) The "average-gain-plus-additive-noise" model of the 1-bit quantizer can be misleading as regards its nonlinearities, even though it may be useful for predicting its stability. We briefly discuss this issue. (c) Some undithered modulators clearly show the production of subharmonic tones. We study the conditions under which this occurs. (d) We also have some observations about why the integrated spectrum of many undithered 1-bit modulators is precisely conjugate-even about fS/4. (e) The idle tone in a 3-level (i.e., 11/2-bit) sigma-delta modulator manifests itself in a different way from that in a 2-level modulator. We study the effect of dither in suppressing the idle tone in both these topologies.

@article{vanderkooy2002towards,
author={vanderkooy, john and lipshitz, stanley p.},
journal={journal of the audio engineering society},
title={towards a better understanding of 1-bit sigma-delta modulators - part 3},
year={2002},
volume={},
number={},
pages={},
doi={},
month={april},}
@article{vanderkooy2002towards,
author={vanderkooy, john and lipshitz, stanley p.},
journal={journal of the audio engineering society},
title={towards a better understanding of 1-bit sigma-delta modulators - part 3},
year={2002},
volume={},
number={},
pages={},
doi={},
month={april},
abstract={this is part 3 of our ongoing investigation into the behaviour of 1-bit sigma-delta modulators. it addresses the following topics: (a) angus has claimed that an undithered 1-bit sigma-delta modulator is effectively self-dithered by its internal noise. we show that his conclusion is essentially a quasi-dc one, and that his pictures of self-dither, although suggestive, do not in fact signify the elimination of all correlated artefacts in the way achieved by a properly-dithered multi-bit modulator. (b) the "average-gain-plus-additive-noise" model of the 1-bit quantizer can be misleading as regards its nonlinearities, even though it may be useful for predicting its stability. we briefly discuss this issue. (c) some undithered modulators clearly show the production of subharmonic tones. we study the conditions under which this occurs. (d) we also have some observations about why the integrated spectrum of many undithered 1-bit modulators is precisely conjugate-even about fs/4. (e) the idle tone in a 3-level (i.e., 11/2-bit) sigma-delta modulator manifests itself in a different way from that in a 2-level modulator. we study the effect of dither in suppressing the idle tone in both these topologies.},}

TY - paper
TI - Towards a Better Understanding of 1-Bit Sigma-Delta Modulators - Part 3
SP -
EP -
AU - Vanderkooy, John
AU - Lipshitz, Stanley P.
PY - 2002
JO - Journal of the Audio Engineering Society
IS -
VO -
VL -
Y1 - April 2002
TY - paper
TI - Towards a Better Understanding of 1-Bit Sigma-Delta Modulators - Part 3
SP -
EP -
AU - Vanderkooy, John
AU - Lipshitz, Stanley P.
PY - 2002
JO - Journal of the Audio Engineering Society
IS -
VO -
VL -
Y1 - April 2002
AB - This is Part 3 of our ongoing investigation into the behaviour of 1-bit sigma-delta modulators. It addresses the following topics: (a) Angus has claimed that an undithered 1-bit sigma-delta modulator is effectively self-dithered by its internal noise. We show that his conclusion is essentially a quasi-dc one, and that his pictures of self-dither, although suggestive, do not in fact signify the elimination of all correlated artefacts in the way achieved by a properly-dithered multi-bit modulator. (b) The "average-gain-plus-additive-noise" model of the 1-bit quantizer can be misleading as regards its nonlinearities, even though it may be useful for predicting its stability. We briefly discuss this issue. (c) Some undithered modulators clearly show the production of subharmonic tones. We study the conditions under which this occurs. (d) We also have some observations about why the integrated spectrum of many undithered 1-bit modulators is precisely conjugate-even about fS/4. (e) The idle tone in a 3-level (i.e., 11/2-bit) sigma-delta modulator manifests itself in a different way from that in a 2-level modulator. We study the effect of dither in suppressing the idle tone in both these topologies.

This is Part 3 of our ongoing investigation into the behaviour of 1-bit sigma-delta modulators. It addresses the following topics: (a) Angus has claimed that an undithered 1-bit sigma-delta modulator is effectively self-dithered by its internal noise. We show that his conclusion is essentially a quasi-dc one, and that his pictures of self-dither, although suggestive, do not in fact signify the elimination of all correlated artefacts in the way achieved by a properly-dithered multi-bit modulator. (b) The "average-gain-plus-additive-noise" model of the 1-bit quantizer can be misleading as regards its nonlinearities, even though it may be useful for predicting its stability. We briefly discuss this issue. (c) Some undithered modulators clearly show the production of subharmonic tones. We study the conditions under which this occurs. (d) We also have some observations about why the integrated spectrum of many undithered 1-bit modulators is precisely conjugate-even about fS/4. (e) The idle tone in a 3-level (i.e., 11/2-bit) sigma-delta modulator manifests itself in a different way from that in a 2-level modulator. We study the effect of dither in suppressing the idle tone in both these topologies.

Authors:
Vanderkooy, John; Lipshitz, Stanley P.
Affiliation:
Audio Research Group, University of Waterloo, Waterloo, Ontario, Canada
AES Convention:
112 (April 2002)
Paper Number:
5620
Publication Date:
April 1, 2002Import into BibTeX
Subject:
Signal Processing Forum
Permalink:
http://www.aes.org/e-lib/browse.cfm?elib=11342