Abstract
The autocorrelation and covariance methods are the two most popular analysis techniques for linear predictive coding of speech. Recent work on the covariance method has utilized the Cholesky decomposition for solving the normal equations. A set of intermediate parameters in the Cholesky approach closely resembles the reflection coefficients in the autocorrelation method, and some workers have treated them as such since several computational and operational advantages thus accrue. The Cholesky decomposition is examined in this paper, and it is shown that when the covariance matrix is not Toeplitz, the intermediate parameters are not the reflection coefficients and do not behave like the reflection coefficients. It is also shown that when the covariance matrix is Toeplitz and the vector of dependent variables consists of autocorrelation terms, the intermediate parameters can be interpreted as reflection coefficients.
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