Linear predictive analysis of speech using non-Toeplitz autocorrelation matrices.
Mitsuo Komura · Journal of the Acoustical Society of Japan (E) · 1986
A covariance method is proposed to analyze speech more accurately than an autocorrelation method. The new covariance method, called the non-Toeplitz form method, ensures uniqueness and stability of data analysis. First, forward and backward prediction models are presented. The uniqueness of definitions of a data vector and a prediction error vector is proved. Second, prediction procedures based on Gram-Schmidt orthogonalization are discussed, and new sample autocorrelation functions are defined. Third, prediction procedures for solving normal equations by using matrix decomposition are presented. An equivalence relationship between auxiliary variables in this procedure and PARCOR coefficients is also discussed. Fourth, the positive definiteness of an autocorrelation matrix whose elements are given by the autocorrelation function proposed in this paper is shown. Finally, the proposed method is compared with other methods.