  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.
