Wiener filters in canonical coordinates for transform coding, filtering, and quantizing

Abstract

Canonical correlations are used to decompose the Wiener filter into a whitening transform coder, a canonical filter, and a coloring transform decoder. The outputs of the whitening transform coder are called canonical coordinates; these are the coordinates that are reduced in rank and quantized in our finite-precision version of the Gauss-Markov theorem. Canonical correlations are, in fact, cosines of the canonical angles between a source vector and a measurement vector. They produce new formulas for error covariance, spectral flatness, and entropy.