Statistical design of analysis/Synthesis systems with quantization

A statistical model is used for the optimal design of analysis/synthesis systems which include quantization of the signals in the separate bands. Two error measures are used. One is a generalization of the usual statistical mean square error (MSE) to time-varying systems (since analysis/synthesis systems with decimation and interpolation are time varying). The second measure is the time average of the expected ℓ2distance between the output of the analysis stage and the analyzed reconstructed signal. The proposed design methods are based on minimizing these error measures and shown to apply not only with the DFT but also with any linear regular transform (e.g. Hadamard, DCT). The above two error measures are shown to be equivalent for a wide class of transforms (including the DFT). The design methods is applicable to either finding an optimal synthesis window for a given analysis window, or finding an optimal analysis window for a given synthesis window. The optimal windows (filters) are obtained by solving a set of linear equations. An optimal analysis/synthesis system is obtained using an iterative algorithm which is based on alternately solving these two sets of linear equations. When no quantization is applied the new design methods coincides with previously reported methods.