Design of compandor quantizer using spline approximations

Abstract

In this paper, the approximation of the optimal compressor function using spline functions of the first and second degree is done. Coefficients on which we form approximative spline functions are determined in two ways: by solving equation systems that are formed from treshold condition and by minimization mean square error (MSE). On the basis of the obtained approximate spline functions, a quantizer designing is done. In order to reduce realization complexity of the designed model, in this paper it is proposed that the optimal compressor function in different segments is approximated by different spline functions. Also, the optimization of quantizer's segment threshold is done. 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). It is shown that by quantizer models proposed in this paper the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved.