Optimality of Orthonormal Transforms for Subband Coding

Theory of optimal orthonormal filter banks has recently been developed under the assumption that quantizers operate at high bit rates. We show that the theory can be simplified if a more general model for quantizers is used. With such a model, we show that principal component filter banks (PCFB) are optimal for orthonormal subband coding under all bit rates and bit allocation strategies. This establishes the link between two fundamental problems: principal component representation of signals and optimal orthonormal subband coding. In block transform case, the Karhunen-Loeve transform is a PCFB. At the other extreme, PCFB’s with ideal filters have recently been constructed. In the intermediate case of FIR orthonormal filter banks, it has recently been shown that there does not always exist a PCFB for a given input. This case is addressed in this paper with some new insights.