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

Author

Scharf, Louis L. ; Thomas, John K.

Author_Institution

Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA

Volume

46

Issue

3

fYear

1998

fDate

3/1/1998 12:00:00 AM

Firstpage

647

Lastpage

654

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

Keywords

Markov processes; Wiener filters; adaptive filters; adaptive signal processing; correlation methods; decoding; entropy; filtering theory; matrix decomposition; quantisation (signal); singular value decomposition; transform coding; Gauss-Markov theorem; Wiener filters; adaptive canonical coordinates; angles; canonical correlations; canonical filter; coherence matrix; coloring transform decoder; entropy; error covariance; filtering; measurement vector; quantization; singular value decomposition; source vector; spectral flatness; transform coding; whitening transform coder; Adaptive filters; Coordinate measuring machines; Decoding; Entropy; Filtering; Gaussian processes; Matrix decomposition; Transform coding; Vectors; Wiener filter;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.661332

Filename

661332