A Study on Asymptotic Characteristics of Scalar Quantizers
- 발행기관 Ajou University, Graduate School
- 지도교수 Sangsin Na
- 발행년도 2012
- 학위수여년월 2012. 8
- 학위명 박사
- 학과 및 전공 일반대학원 전자공학과
- 실제URI http://www.dcollection.net/handler/ajou/000000012657
- 본문언어 영어
- 저작권 아주대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
Asymptotic characteristics of scalar quantizers are investigated in this study. The covered quantizers are symmetric uniform and symmetric nonuniform quantizers optimized for the sources with specific probability densities with zero-mean and unit-variance including the two-sided Rayleigh, the normal, the Laplace, the gamma, the Bucklew-Gallagher, and the Hui-Neuhoff distributions. Although the resulting nonuniform quantizers optimized for the latter three distributions are not symmetric with even numbers of quantization points, only nonnegative half part was considered in the study since the effect of asymmetry vanishes as the number of quantization points increases. The covered asymptotic characteristics of an optimal quantizer are the innermost threshold, the outermost threshold, the inner distortion, the outer distortion, and the total distortion. To verify the results from the asymptotic analyses, optimal quantizers for the considered distributions have been designed for bit rates up to 20 (hence 2^20=1,048,576 quantization points) for uniform quantizers and 16 (hence 2^16=65,536 quantization points) for nonuniform quantizers. It is concluded that the asymptotic formulas for the characteristics of optimal/mismatched and uniform/nonuniform quantizers are generally consistent with the observed numerical results from the designed quantizers. Also, the high resolution numerical data obtained from the designed quantizers can be useful as references for possible future theoretical analyses of symmetric scalar quantizers.
more목차
Acknowledgement
Abstract
List of Figures
List of Tables
List of Symbols
1. Introduction
1.1 Overview
1.2 Asymptotic Analysis
1.3 Scalar Quantizers
1.4 Source Distributions of Interest
2. Optimal Scalar Quantizers
2.1 Optimal Uniform Quantizers
2.2 Optimal Nonuniform Quantizers
3. Mismatched Scalar Quantizers
3.1 Mismatched Uniform Quantizers
3.2 Mismatched Nonuniform Quantizers
4. Numerical Results
4.1 Implementation
4.2 Optimal Uniform Quantizers
4.3 Optimal Nonuniform Quantizers
4.4 Mismatched Uniform Quantizers
4.5 Mismatched Nonuniform Quantizers
5. Conclusions
A. Numerical Tables
B. Source Codes in MATLAB
Bibliography
Index
