Sliding windows and lattice algorithms for computing QR factors in the least squares theory of linear prediction

The authors 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 it is possible to perform QR factorization of 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., The QR and Cholesky algorithms generate generalized reflection coefficients that may be used in the usual ways for analysis, synthesis, or classification