Asymptotic Analysis of Switched Uniform Polar Quantization for Memoryless Gaussian Source

This letter performs an asymptotic analysis of the switched uniform polar quantizer (SUPQ) composed of $k$ asymptotically optimal unrestricted uniform polar quantizers designed for the memoryless Gaussian source. The closed-form formulas are derived for signal to quantization noise ratio (SQNR) and the number of phase levels of the quantizers constituting the SUPQ. It is studied how SQNR depends on the variance mismatch and the number of quantizers $k$. It is shown that with a log-uniform distribution of the variances for which the quantizers constituting the SUPQ are designed one can reduce the variance range of average-taking of SQNR.

I. Introduction

Fixed-Rate quantizers designed for a particular variance are not suitable for the quantization of non-stationary signals that, as well as speech or image signals, have changing variance characteristics [1]. In such situations, in spite of the fact that designed-for and applied-to sources can be of the same family of probability density functions (PDFs), the variance mismatch between the input signal's variance and the variance for which the quantizer is designed occurs very often [2]–[4].