Perfect-reconstruction FIR filter banks with mirror-image symmetry

In this paper, the problem of designing an N-band perfect-reconstruction FIR analysis/synthesis system given K of the analysis filters (referred to as the (N, K)-problem) is treated in the context of pairwise mirror-image symmetric filter banks, and it is shown to be equivalent to two independent, unconstrained (N/2,K/2)-problems. The synthesis bank, which is shown to have the mirror-image symmetry too, is easily obtained as a byproduct of the solution process. A complete parametrization of the resulting filters is given, and an optimization procedure, leading to practically useful filters, is discussed. The linear phase (LP) case is also treated, and a complete parametrization of the LP analysis/synthesis polyphase matrices is presented. The proposed approach leads naturally to a ladder-type realization of the filter bank, with the PR, LP, and mirror-image symmetry properties being structurally enforced under both coefficient quantization and round-off errors. A design example is given to demonstrate the results of the paper.