  In this paper we present a method to design paraunitary polyphase matrices of
critically sampled rational filter banks. The method is based on (P,Q)
shift-invariant systems, and so any kind of rational splitting of the frequency
spectrum can be achieved using this method. Ideal (P,Q) shift-invariant system
with smallest P and Q that map of a band of input spectrum to the output
spectrum are obtained. A new set of filters is obtained that characterize a
(P,Q) shift-invariant system. Ideal frequency spectrum of these filters are
obtained using ideal $(P,Q)$ shift-invariant systems. Actual paraunitary
polyphase matrices are then obtained by minimizing the stopband energies of
these filters against the parameters of the paraunitary polyphase matrices.
