Numerical determination of the optimal value of quantizer's segment threshold using quadratic spline functions

7 1 Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia 8 2 Department of Telecommunications, Faculty of Electronic Engineering, 9 University of Niš, Serbia 10 3 Mathematical Department, Faculty of Occupational Safety, University of Niš, Serbia 11 12 13 14 . 15 ABSTRACT 16 17 In this paper, an approximation of the optimal compressor function using the quadratic spline functions has been presented. The coefficients of the quadratic spline functions are determined by minimizing the mean-square error (MSE). Based on the obtained approximative quadratic spline functions, the design for companding quantizer for Gaussian source is done. The support region of proposed companding quantizer is divided on segments of unequal size, where the optimal value of segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). It is shown that by the companding quantizer proposed in this paper, the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved. 18