On determining partial correlation coefficients by the covariance method of linear prediction

Partial correlation coefficients of speech samples (sometimes called reflection coefficients) are an important set of parameters in linear prediction analysis of speech and have proved to be useful for many practical applications, such as speech encoding, speech synthesis‐by‐rule, etc. So far, it has been thought [Gibson, IEEE Trans. ASSP, p. 93 (Feb. 1977)] that the covariance method does not provide a direct method of computing the partial correlations unless the covariance matrix is a Toeplitz matrix. Indirect computation of partial correlations from the predictor coefficients have obvious disadvantages. It will be shown that the partial correlation coefficients are indeed obtained as a set of intermediate parameters by the covariance method even when the covariance matrix is non‐Toeplitz. These intermediate parameters are obtained as a solution of a set of linear equations through Choleski decomposition of the covariance matrix and, after appropriate normalization, are transformed to the partial corre...