Optimal nonuniform orthonormal filter banks for subband coding and signal representation

It has been shown that principal component filter banks (PCFB) are optimum orthonormal filter banks for subband coding for the uniform case in which all decimation ratios are the same. In this paper we present the analogous results for the nonuniform case. In contrast to the uniform case where there is only one PCFB, there are more than one PCFB in the nonuniform case. For a fixed set of decimation ratios, there are as many PCFB as the total number of permutations of the decimation ratios. For a fixed number of channels M, we show that there are finitely many sets of decimation ratios that a nonuniform filter bank can have. We show that one of the PCFB corresponding to a particular set of decimation ratios with a particular permutation is an optimum M-channel nonuniform orthonormal filter bank for subband coding. As in the uniform case, the results are valid at arbitrary bit rates