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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.

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Subject

matrix algebra
least squares approximations
filtering and prediction theory

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