Bases for the whole sample symmetric filter banks using a complex allpass filter

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.