On perfect-reconstruction FIR filter banks

This paper deals with the problem of designing an TV-band maximally-decimated analysis filter bank given K of its filters, so that perfect reconstruction with FIR synthesis filters is possible. An algorithm for computing the N-K unknown analysis filters and the synthesis filters is given and the solution set is completely parametrized. The parametrization is exploited in optimizing the frequency responses of the resulting filters and to derive also a simple parametrization for the paraunitary case. The linear-phase case is also discussed with emphasis on the 2-band filter banks. An example is provided to illustrate the theory.