Least squares filters in canonical coordinates for transform coding, filtering, and quantizing

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, and these are the coordinates that are reduced in rank and coded in a quantized version of the Gauss-Markov theorem. Canonical correlations produce new formulas for error covariance, spectral flatness, and entropy and lead to plausible definitions of angles between random vectors in a stochastic setting. Adaptive canonical coordinates suggest an approach to channel equalization.