Piecewise Uniform Quantization for One-Dimensional Two-Component GMM

In this paper we propose piecewise uniform scalar quantization (PUSQ) for amplitudes having one dimensional two-component Gaussian mixture model probability density function (GMM pdf). For the proposed model we also derive asymptotic formulas for the mean-square error (distortion D) and signal to quantization noise ratio (SQNR). In addition, for the constraints introduced during the theoretical model formulation, we perform a numerical optimization of PUSQ in terms of the mean square-error, or, equivalently, in terms of the SQNR. In particular, for the given constraints we determine the threshold between ranges of PUSQ that maximizes the SQNR. As quantization of amplitudes with GMM pdf has not been frequently considered in the literature, we believe that the results presented in this paper will help to gain a better insight into this issue.