On optimal analysis/synthesis filters for coding gain maximization

We consider the use of pre and postfilters in conjunction with M-channel, uniform-hand paraunitary (orthonormal) filter banks. We show that given any orthonormal filter bank, the pre and postfilters that maximize the coding gain are determined entirely by the power spectrum of the input process regardless of the details of the orthainormal filter bank (which could be FIR, IIR, or even the ideal brickwall filter bank). The optimized coding gain, however, depends on the prefilter as well as the sandwiched orthonormal filter bank. The coding gain improvement due to pre and postfiltering is often significant as we demonstrate with numerical examples and comparisons. The validity of our results depends strongly on the orthonormality property of the filter bank in between the pre and postfilters. In the nonorthonormal case, most of these results are not true, as is demonstrated.