Statistical design of analysis/synthesis systems with quantization

A statistical model is used for the optimal design of analysis/synthesis systems that include quantization of the signals in separate bands. Two types of quantization approaches are analyzed: fine quantization modelled by additive noise, and matrix quantization. With proper modification, the model applies to other types of quantization approaches. Assuming that the system operates as a waveform coder, two error measures are used: a generalization of the usual statistical mean-square error (MSE) to time-varying systems, and the MSE between the outputs of the analysis of the original and reconstructed signals. The measures are shown to be equivalent. A method that is applicable to the design of optimal synthesis filters, given the analysis filters, is presented. For fine quantization, an iterative algorithm for the design of an optimal analysis/synthesis system is presented, together with its convergence properties. If no quantization is applied, the results obtained with the presented method coincide with previously reported results