Solution of the Lloyd-Max quantizer parameters by the method of successive substitution
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Authors
Moose, Paul H.
Bassiouni, A-A. M.
Subjects
Advisors
Date of Issue
1987-10
Date
1987-10
Publisher
Monterey, CA; Naval Postgraduate School
Language
en_US
Abstract
The method of successive substitution is shown applicable to solve for the classical minimum distortion quantizer parameters. The method is self converging and parameters can be calculated to any desired accuracy. The minimum distortion quantizer parameters, as well as parameters based on other criterion such as quantizers for signal detection, minimum risk quantizers and quantizers for LMMS estimation can be solved by Max's trial and error technique. There are also many other approximation methods to calculate the quantizer parameters. This report applies the method of successive substitution and its modifications to solve for the Lloyd-Max quantizer parameters. It is more accurate and computationally more efficient than the previously reported methods. It is shown to easily generate 7 bit (128 level) optimum quantization. The Lloyd-Max minimum mean square distortion quantizer problem deals with transforming a random variable X of differentiable probability density function f(x) into the N-level discrete random variable Y
Type
Technical Report
Description
Series/Report No
Organization
Graduate School of Engineering and Applied Science (GSEAS)
Research and Sponsored Programs Office (RSPO)
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
NPS-62-88-004
Sponsors
Funder
Format
35 p. ; 28 cm.
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.