Rate-Distortion-Optimal Subband Coding Without Perfect-Reconstruction Constraints

We investigate the design of subband coders without the traditional perfect-reconstruction constraint on the filters. The coder uses scalar quantizers, and its filters and bit allocation are designed so as to optimize a rate-distortion criterion. Our results hold for a broad class of ratedistortion criteria that satisfy certain convexity properties. We begin by showing that optimality can be achieved using filter banks that are the cascade of a (paraunitary) principal component filter bank for the input spectral process and a set of pre-- and post--filters surrounding each quantizer. Analytical expressions for the pre- and postfilters are then derived. An algorithm for computing the globally optimal filters and bit allocation is given. We also develop closedform solutions for the special case of two-channel coders under an exponential rate--distortion model. Finally, we investigate a constrained-length version of the filter design problem, which is applicable to practical coding scena..