On bit allocation strategies for paraunitary subband coders

Quadrature mirror filters have been employed to decompose a signal into subbands. The signals in each subband are quantized before transmission. The authors derive conditions on the individual quantizer error variances so as to minimize the overall reconstruction error variance. The present results hold for filter banks having paraunitary polyphase matrices. Under the assumption that the total number of bits over all channels is fixed, it is shown that their distribution which minimizes the reconstruction error variance is the one that makes the individual quantizer variances equal. This analysis is extended to tree-structured filter banks, such as those used for generating orthonormal wavelets. In this case, it is shown that the quantizer error variance in a particular branch should be proportional to the corresponding decimation factor