General least-squares design of allpass transformed DFT filter-banks

The allpass transformation is a common approach to design a frequency warped analysis-synthesis filter-bank (AS FB) with non-uniform time-frequency resolution. Such filter-banks are beneficial, e.g., for speech and audio subband processing, but their synthesis filter-bank design is more complex as for uniform filter-banks. This problem is tackled by a new least-squares error (LS) synthesis filter-bank design. Magnitude and phase distortions are minimized with the constraints for complete aliasing cancellation and a restricted signal delay. The coefficients of the synthesis filters are determined by a linear set of equations with linear constraints which can be easily solved. The obtained FIR synthesis subband filters exhibit a frequency selectivity similar to that of the IIR analysis filters. The new concept is very general and can be applied in case of an allpass transformation of first or higher order as well as for polyphase network (PPN) filter-banks where the prototype filter length exceeds the number of channels. These properties make the proposed design of interest for various subband processing systems requiring non-uniform frequency bands.