An Optimal Biorthogonal M-Channel Signal Matched FIR Filter Bank

This paper deals with the problem of finding an optimum M-channel biorthogonal signal adapted filter bank. The concept of Principal Component Filter Bank (PCFB) has been proposed, independently by many researchers, as the optimal solution for signal adapted filter banks. PCFB, however, exist only for three special cases of orthonormal filter banks: for the class of transform coders, for 2-channel subband coders and for sub-band coders with unconstrained filters. Although various rigorous approximations for practically realizable PCFBs have also been proposed, but they are only sub-optimal. In this work, we present a biorthogonal M-channel signal matched FIR filter bank which satisfies the properties of spectral majorization and total decorrelation, thus yields optimum coding gain, for any class of sub-band coders. The design strategy does not assume the input statistics to be WSS. To validate the theory, the performance of the proposed algorithm has been compared with the existing literature, using simulations.