CODING GAIN IN PARAUNITARY ANALYSIS SYNTHESIS SYSTEMS

Subband coders have been used in the past to decompose a signal into subbands. The signals in each subband are quantized before transmission. The problem of optimal bit allocation involves allocating bits to the individual quantizers from a fixed budget so as to minimize the overall reconstruction error variance. The problem has been addressed in the past for two cases, namely orthogonal transform coding, and ideal brick-wall filtering. Both of these are special cases of the so-called ''paraunitary'' filter banks. The results which were proved for these special cases have been used without proof for other nonparaunitary subband coding,schemes. We present here a formal proof that these bit-allocation results hold for the entire class of paraunitary subband coders. Next, we address the problem of finding an optimal paraunitary subband coder, so as to maximize the coding gain of the system. We then analyze the bit-allocation problem for the case of paraunitary tree-structured filter banks, such as those used for generating orthonormal wavelets. The even more general case of nonuniform filter banks is next considered. In all cases we show that under optimal bit allocation, the variance of the errors introduced by each of the quantizers have to be equal. Expressions for coding gains for these systems have also been derived.