Abstract
In this paper, the optimization of quantizer’s segment threshold is done. The quantizer is designed on the basis of approximative spline functions. Coefficients on which we form approximative spline functions are calculated by minimization mean square error (MSE). For coefficients determined in this way, spline functions by which optimal compressor function is approximated are obtained. For the quantizer designed on the basis of approximative spline functions, segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). Thus, quantizer with optimized segment threshold is achieved. It is shown that by quantizer model designed in this way and proposed in this paper, the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved.
Highlights
Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set—such as rounding values to some unit of precision
Coefficients on which we form approximative spline functions are calculated by minimization mean square error (MSE)
For the quantizer designed on the basis of approximative spline functions, segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR)
Summary
Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set—such as rounding values to some unit of precision. A comprehensive analysis of SQNR behavior in a wide range of variances for the piecewise uniform scalar quantizer PUSQ designed for a Laplacian source according to the piecewise linear approximation to the optimal compressor law is reported in [4]. Quantizer designed on the basis of approximative spline functions, whose support region is divided on segments of equal size is described in [7]. Depending on value of optimized segment threshold, approximate spline functions, by which the optimal compressor function is approximated, are determined. In the papers mentioned above, the influence of support region choice on scalar quantizer performances that are designed for Laplacian source is analysed. By designing the proposed quantizer based on approximate spline functions and optimized threshold segment, SQNR that is close to that of the nonlinear optimal companding quantizer is obtained.
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