Optimized orthonormal transforms for SNR improvement by subband processing

Orthonormal transforms for signal representation are ubiquitous in a large number of signal processing and communications problems. A problem that frequently arises is to find the best transform for a particular situation. This paper considers the problem of noise suppression by subband processing. The noisy input is split into separate frequency bands using an orthogonal transform or filter-bank (FB), and these bands are separately denoised. We address the problem of finding the best FB for such a scheme. We have previously pointed out a strong connection between optimality of the FB and the principal component property, which in particular solves this problem when the noise is white. Here we establish results for the case when the noise is colored. We prove that if a common principal component filter-bank (PCFB) for the signal and the noise exists, it is optimal within the class of memoryless transforms. We show how this result need not be true for more general classes, using the class of all (unconstrained) FBs as an illustration