Construction of Optimal Uniform Polar Switched Quantizer in Wide Volume Range

In this paper we will present a simple and complete asymptotical analysis of optimal uniform quantization of two- dimensional memoryless Gaussian sources with the respect to distortion (D(sigma,sigma₀)) i.e., the mean-square error (MSE). Uniform quantizer optimality conditions and all main equations for phase partitions and optimal number of levels for each partition are presented. We derive the optimal granular distortion D_g ^opt (sigma,sigma₀) in a closed form. Switched quantization is used in order to give higher quality by increasing signal-to-quantization-noise-ratio (SQNR) in a wide range of signal volumes (variances).