Sliding windows and lattice algorithms for computing QR factors in the least squares theory of linear prediction
Date
1990
Authors
Scharf, Louis L., author
Demeure, Cédric, author
IEEE, publisher
Journal Title
Journal ISSN
Volume Title
Abstract
In this correspondence we pose a sequence of linear prediction problems that differ a little from those previously posed. The solutions to these problems introduce a family of "sliding" window techniques into the least squares theory of linear prediction. By using these techniques we are able to QR factor the Toeplitz data matrices that arise in linear prediction. The matrix Q is an orthogonal version of the data matrix and the matrix R is a Cholesky factor of the experimental correlation matrix. Our QR and Cholesky algorithms generate generalized reflection coefficients that may be used in the usual ways for analysis, synthesis, or classification.
Description
Rights Access
Subject
matrix algebra
least squares approximations
filtering and prediction theory