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

TL;DR

This paper introduces a method to numerically determine the optimal segment threshold for a quantizer using quadratic spline functions, enhancing signal-to-noise ratio performance for Gaussian sources.

Contribution

It presents a novel approach to approximate the optimal compressor function with quadratic splines and determines the best segment thresholds numerically for improved quantizer design.

Findings

Achieves SQNR close to nonlinear optimal quantizer

Provides a numerical method for optimal segment threshold determination

Demonstrates improved quantizer performance for Gaussian sources

Abstract

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.