Polynomial transform implementation of digital filter banks

This paper investigates the use of polynomial transforms for the implementation of uniform digital bandpass filter banks. The technique is based upon a decomposition of the N bandpass filters into a set of real polyphase filters followed by a DCT (discrete cosine transform) of size N. The DCT is converted into a DFT (discrete Fourier transform) of size N and the polyphase filters are evaluated by DFT's. This procedure yields a two-dimensional DFT which is computed by a polynomial transform and odd DFT's. We show that this technique reduces significantly the number of arithmetic operations when compared to conventional methods, and yields a regular structure in which most of the computations are performed with FFT-type algorithms.