Statistically optimal synthesis banks for subband coders

In maximally decimated filter banks, the perfect reconstruction or biorthogonal solution is not necessarily the best choice when subband quantizers are present. Under suitable statistical assumptions, expressions for the best synthesis bank can be derived in terms of the analysis bank and other statistical quantities. We explore this topic for subband coders and the special case of transform coders. We highlight the statistical conditions under which the biorthogonal solution is still the best. We derive expressions for the Wiener filter matrix in terms of the joint statistics of appropriate signals. Special cases where the optimal synthesis filter bank is the biorthogonal system followed by a scalar post filter are also considered