Lattice Algorithms for Computing QR and Cholesky Factors in the Least Squares Theory of Linear Prediction
COLORADO UNIV AT BOULDER DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
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This paper poses a sequence of linear prediction problems that are a little different from those previously posed. By solving the sequence of problems we are able to QR factor data matrices of the type usually associated with correlation, pre and post-windowed, and covariance methods of linear prediction. Our solutions cover the forward, backward, and forward-backward problems. The QR factor orthogonalizes the data matrix and solves the problem of Cholesky factoring the experimental correlation matrix and its inverse. This means we may use generalize Levinson algorithms to derive generalized QR algorithms, which are then used to derive generalized Schur algorithms. All three algorithms are true lattice algorithms that may be implemented either on a vector machine or on a multi-tier lattice, and all three algorithms generate generalized reflection coefficients that may be used for filtering or classification. Keywords Toeplitz matrices Factorization Covariance Matrix theory.
- Theoretical Mathematics