BASES FOR THE WHOLE SAMPLE SYMMETRIC FILTER BANKS USING A COMPLEX ALLPASS FILTER

摘要

This work is concerned with the design problem of a whole sample symmetric filter bank where the lowpass and highpass filters are defined in terms of a complex allpass filter. The design problem reduces to the evaluation of the coefficients of this allpass filter. The regularity requirement of the filter bank leads to a set of flatness constraints. The required frequency selectivity of the filters is expressed as another set of constraints. The combined set of constraints leads to a generalized eigenvalue problem that can be reduced to a regular eigenvalue problem by conjecturing a certain matrix to be nonsingular. The eigenvector corresponding to the largest positive eigenvalue of the last problem is the sought vector of the coefficients of the allpass filter. Since the extremal frequencies of the frequency response are not known beforehand, the Remez exchange algorithm is applied to reach the solution.