An iterative method for designing orthogonal two-channel FIR filter banks with regularities

An efficient iterative method is described for designing orthogonal two-channel perfect-reconstruction FIR filter banks in such a way that the low-pass analysis filter has the given number of fixed zeros at z=-1 and its energy in the given stopband region is minimized. When using the resulting two-channel filter bank for generating discrete-time wavelet banks, the number of vanishing moments is equal to the number of zeros being located at z=-1. The proposed design scheme is fast and the convergence to the optimum solution is independent of the starting-point filter bank. Compared to the two-channel filter bank equivalents designed in the minimax sense as proposed by Rioul and Duhamel (1994), the regularities of the resulting wavelets are increased and the stopband energies of the subfilters are decreased. If there are no constraints on the number of zeros at z=-1, then the resulting banks are useful building blocks in generating frequency-selective multi-channel filter banks and octave filter banks.