Authors: Nikolić, Jelena
Perić, Zoran
Velimirović, Lazar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Simple Solution for Designing the Piecewise Linear Scalar Companding Quantizer for Gaussian Source
Journal: Radioengineering
Volume: 22
Issue: 1
First page: 194
Last page: 199
Issue Date: 1-Apr-2013
Rank: M23
ISSN: 1210-2512
To overcome the difficulties in determining an inverse compressor function for a Gaussian source, which appear in designing the nonlinear optimal companding quantizers and also in the nonlinear optimal companding quantization procedure, in this paper a piecewise linear compressor function based on the first derivate approximation of the optimal compressor function is proposed. We show that the approximations used in determining the piecewise linear compressor function contribute to the simple solution for designing the novel piecewise linear scalar companding quantizer (PLSCQ) for a Gaussian source of unit variance. For the given number of segments, we perform optimization procedure in order to obtain optimal value of the support region threshold which maximizes the signal to quantization noise ratio (SQNR) of the proposed PLSCQ. We study how the SQNR of the considered PLSCQ depends on the number of segments and we show that for the given number of quantization levels, SQNR of the PLSCQ approaches the one of the nonlinear optimal companding quantizer with the increase of the number of segments. The presented features of the proposed PLSCQ indicate that the obtained model should be of high practical significance for quantization of signals having Gaussian probability density function.
Keywords: Compressor function | Piecewise linear scalar companding quantizer | Support region threshold optimization
Publisher: Brno University of Technology
Project: Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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