New results on cosine-modulated FIR filter banks satisfying perfect reconstruction

The authors present a derivation of the necessary and sufficient condition on the polyphase components of a linear-phase prototype (length N=2 mM) such that the polyphase component matrix of the filter bank is lossless. This in turn ensures that the modulated filter bank satisfies the PR (perfect reconstruction) property. An efficient design procedure (which involves fewer parameters to be optimized than other approaches) is presented. By this approach, FIR (finite-impulse-response) PR filter banks can be designed for an arbitrary number of channels. Moreover, since both the analysis and synthesis filter banks are obtained by modulation, they can be implemented very efficiently (using the discrete cosine transform). The design procedure is outlined and a design example is presented