Minimum mean square error nonuniform FIR filter banks

A theory for jointly optimizing nonuniform analysis and synthesis FIR filter banks with arbitrary filter lengths and an arbitrary delay through the filter bank is developed. The FIR subband coder is optimized with respect to the minimum mean square error between the output and the input signals under a bit constraint. The subband quantizers are modeled as additive noise sources. Theoretical comparisons are made against a well-known 5-3 wavelets used in a tree-structure. The proposed filter banks, which are both rate- and source-dependent, have a better distortion rate performance. Equations for finding jointly optimized analysis and synthesis filter banks under a power constraint are also presented.