Algorithm for Jointly Optimized Analysis and Synthesis Fir Filter Banks

An algorithm for jointly optimizing uniform analysis and synthesis FIR filter banks for a given input power spectral density is proposed. The FIR subband coder is optimized with respect to the minimum block mean square error between the output and the input signals under a bit constraint. The subband quantizers are modeled as additive, signal-independent, white noise sources. Illustrative examples showing the system performance as well as filter magnitude and impulse responses are given. The performance results are compared to the rate distortion curves, the performance for the optimal transform coder, and the optimal filter bank with unconstrained length filters. The use of two subbands in a filter bank having filters of length six in all the filters, gives 1.42 dB better system performance compared to a signal-adaptive, linear phase, biorthogonal filter bank, when coding a Gaussian AR(1) source with correlation coefficient 0.95 at 2.75 bits/sample.