Statistical optimization of PR-QMF banks and wavelets

The design of optimal power complementary filters for multiresolution signal decomposition is considered. As a new performance measure in statistical optimization of filter banks the norm of cross-correlation (all subbands including all delays) will be used for optimization. The obtained filters will be compared to filters having minimum reconstruction error when the high-pass branches are dropped. In the paraunitary case, which is considered here, this reconstruction error is closely related to the coding gain of PCM in subbands over direct PCM. While the KL-transform combines both minimum reconstruction error and perfect decorrelation, filter banks do not. It is clear that the norm of cross-correlation becomes very important when better techniques than PCM are considered for the coding of subband signals