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To overcome the difficulties in determining an inverse compressor functionfor a Gaussian source, which appear in designing the nonlinear optimalcompanding quantizers and also in the nonlinear optimal companding quantizationprocedure, in this paper a piecewise linear compressor function based on thefirst derivate approximation of the optimal compressor function is proposed. Weshow that the approximations used in determining the piecewise linearcompressor function contribute to the simple solution for designing the novelpiecewise linear scalar companding quantizer (PLSCQ) for a Gaussian source ofunit variance. For the given number of segments, we perform optimizationprocedure in order to obtain optimal value of the support region thresholdwhich maximizes the signal to quantization noise ratio (SQNR) of the proposedPLSCQ. We study how the SQNR of the considered PLSCQ depends on the number ofsegments and we show that for the given number of quantization levels, SQNR ofthe PLSCQ approaches the one of the nonlinear optimal companding quantizer withthe increase of the number of segments. The presented features of the proposedPLSCQ indicate that the obtained model should be of high practical significancefor quantization of signals having Gaussian probability density function.

Simple Solution for Designing the Piecewise Linear Scalar Companding Quantizer for Gaussian Source