Designing filters for polyphase filter banks

The paper concerns the filter design problem for a recently-proposed polyphase filter bank with an arbitrary number of subband channels. We develop an analytical formula for the design of a prototype filter used in the polyphase filter bank. Compared with direct numerical design methods, this formula-based method allows the design of the required FIR lowpass prototype filter with a much lower complexity of operation and better filter bank performance. We further extend the theoretical results to two dimensions. Examples are also presented.