Estimation of the Vocal-Tract Shape by Optimum Inverse Filter Processing of Speech

Abstract

It is shown that the filtering process of the optimum inverse filter [J. D. Markel, SCRL Monogr. No. 7, 111 (Oct. 1971)] is identical to the filtering process of the nonuniform acoustic tube model [B. S. Atal and S. L. Hanauer, J. Acoust. Soc. Amer. 50, 637 (1971)] in which the vocal tract is divided into a finite number of sections with equal lengths. The common factor between the two processes is shown to be a set of reflection coefficients. These reflection coefficients are obtained as intermediate results of a recursive solution to the inverse filter equations. Both area functions and filter coefficients can be easily determined from this set of reflection coefficients. The procedure can be realized by recursive digital filters, thus making possible an efficient implementation as a computer program to obtain the time variation of the vocal-tract shape together with the spectral envelope of the speech sample. This procedure simplifies finding the relationships between the vocal-tract shape and its acoustic features, e.g., from the vocal-tract shape to the filter coefficients, from which formant frequencies and bandwidths can be determined, and vice versa. Applications and limitations of this procedure to connected speech are discussed. [The work was supported by the Office of Naval Research.]