IEICE TRANSACTIONS on Communications
A Delta-Sigma Modulator Using a Non-uniform Quantizer Adjusted for the Probability Density of Input Signals
Summary :
A novel delta-sigma modulator that employs a non-uniform quantizer whose spacing is adjusted by reference to the statistical properties of the input signal is proposed. The proposed delta-sigma modulator has less quantization noise compared to the one that uses a uniform quantizer with the same number of output values. With respect to the quantizer on its own, Lloyd proposed a non-uniform quantizer that is best for minimizing the average quantization noise power. The applicable condition of the method is that the statistical properties of the input signal, the probability density, are given. However, the procedure cannot be directly applied to the quantizer in the delta-sigma modulator because it jeopardizes the modulator's stability. In this paper, a procedure is proposed that determine the spacing of the quantizer with avoiding instability. Simulation results show that the proposed method reduces quantization noise by up to 3.8 dB and 2.8 dB with the input signal having a PAPR of 16 dB and 12 dB, respectively, compared to the one employing a uniform quantizer. Two alternative types of probability density function (PDF) are used in the proposed method for the calculation of the output values. One is the PDF of the input signal to the delta-sigma modulator and the other is an approximated PDF of the input signal to the quantizer inside the delta-sigma modulator. Both approaches are evaluated to find that the latter gives lower quantization noise.
- Publication
- IEICE TRANSACTIONS on Communications Vol.E95-B No.7 pp.2257-2265
- Publication Date
- 2012/07/01
- Publicized
- Online ISSN
- 1745-1345
- DOI
- 10.1587/transcom.E95.B.2257
- Type of Manuscript
- PAPER
- Category
- Fundamental Theories for Communications
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Toru KITAYABU, Mao HAGIWARA, Hiroyasu ISHIKAWA, Hiroshi SHIRAI, "A Delta-Sigma Modulator Using a Non-uniform Quantizer Adjusted for the Probability Density of Input Signals" in IEICE TRANSACTIONS on Communications,
vol. E95-B, no. 7, pp. 2257-2265, July 2012, doi: 10.1587/transcom.E95.B.2257.
Abstract: A novel delta-sigma modulator that employs a non-uniform quantizer whose spacing is adjusted by reference to the statistical properties of the input signal is proposed. The proposed delta-sigma modulator has less quantization noise compared to the one that uses a uniform quantizer with the same number of output values. With respect to the quantizer on its own, Lloyd proposed a non-uniform quantizer that is best for minimizing the average quantization noise power. The applicable condition of the method is that the statistical properties of the input signal, the probability density, are given. However, the procedure cannot be directly applied to the quantizer in the delta-sigma modulator because it jeopardizes the modulator's stability. In this paper, a procedure is proposed that determine the spacing of the quantizer with avoiding instability. Simulation results show that the proposed method reduces quantization noise by up to 3.8 dB and 2.8 dB with the input signal having a PAPR of 16 dB and 12 dB, respectively, compared to the one employing a uniform quantizer. Two alternative types of probability density function (PDF) are used in the proposed method for the calculation of the output values. One is the PDF of the input signal to the delta-sigma modulator and the other is an approximated PDF of the input signal to the quantizer inside the delta-sigma modulator. Both approaches are evaluated to find that the latter gives lower quantization noise.
URL: https://global.ieice.org/en_transactions/communications/10.1587/transcom.E95.B.2257/_p
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@ARTICLE{e95-b_7_2257,
author={Toru KITAYABU, Mao HAGIWARA, Hiroyasu ISHIKAWA, Hiroshi SHIRAI, },
journal={IEICE TRANSACTIONS on Communications},
title={A Delta-Sigma Modulator Using a Non-uniform Quantizer Adjusted for the Probability Density of Input Signals},
year={2012},
volume={E95-B},
number={7},
pages={2257-2265},
abstract={A novel delta-sigma modulator that employs a non-uniform quantizer whose spacing is adjusted by reference to the statistical properties of the input signal is proposed. The proposed delta-sigma modulator has less quantization noise compared to the one that uses a uniform quantizer with the same number of output values. With respect to the quantizer on its own, Lloyd proposed a non-uniform quantizer that is best for minimizing the average quantization noise power. The applicable condition of the method is that the statistical properties of the input signal, the probability density, are given. However, the procedure cannot be directly applied to the quantizer in the delta-sigma modulator because it jeopardizes the modulator's stability. In this paper, a procedure is proposed that determine the spacing of the quantizer with avoiding instability. Simulation results show that the proposed method reduces quantization noise by up to 3.8 dB and 2.8 dB with the input signal having a PAPR of 16 dB and 12 dB, respectively, compared to the one employing a uniform quantizer. Two alternative types of probability density function (PDF) are used in the proposed method for the calculation of the output values. One is the PDF of the input signal to the delta-sigma modulator and the other is an approximated PDF of the input signal to the quantizer inside the delta-sigma modulator. Both approaches are evaluated to find that the latter gives lower quantization noise.},
keywords={},
doi={10.1587/transcom.E95.B.2257},
ISSN={1745-1345},
month={July},}
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TY - JOUR
TI - A Delta-Sigma Modulator Using a Non-uniform Quantizer Adjusted for the Probability Density of Input Signals
T2 - IEICE TRANSACTIONS on Communications
SP - 2257
EP - 2265
AU - Toru KITAYABU
AU - Mao HAGIWARA
AU - Hiroyasu ISHIKAWA
AU - Hiroshi SHIRAI
PY - 2012
DO - 10.1587/transcom.E95.B.2257
JO - IEICE TRANSACTIONS on Communications
SN - 1745-1345
VL - E95-B
IS - 7
JA - IEICE TRANSACTIONS on Communications
Y1 - July 2012
AB - A novel delta-sigma modulator that employs a non-uniform quantizer whose spacing is adjusted by reference to the statistical properties of the input signal is proposed. The proposed delta-sigma modulator has less quantization noise compared to the one that uses a uniform quantizer with the same number of output values. With respect to the quantizer on its own, Lloyd proposed a non-uniform quantizer that is best for minimizing the average quantization noise power. The applicable condition of the method is that the statistical properties of the input signal, the probability density, are given. However, the procedure cannot be directly applied to the quantizer in the delta-sigma modulator because it jeopardizes the modulator's stability. In this paper, a procedure is proposed that determine the spacing of the quantizer with avoiding instability. Simulation results show that the proposed method reduces quantization noise by up to 3.8 dB and 2.8 dB with the input signal having a PAPR of 16 dB and 12 dB, respectively, compared to the one employing a uniform quantizer. Two alternative types of probability density function (PDF) are used in the proposed method for the calculation of the output values. One is the PDF of the input signal to the delta-sigma modulator and the other is an approximated PDF of the input signal to the quantizer inside the delta-sigma modulator. Both approaches are evaluated to find that the latter gives lower quantization noise.
ER -
English
