Determining the length and cross-sectional area of the vocal tract jointly from formants using acoustic sensitivity function

A method for determining the length and cross-sectional area of the vocal tract from target formants is presented. The area function was approximated by summing several mode functions to reduce the number of degrees of freedom among the area parameters. Furthermore, the tract length was represented as a function of the coefficients for two principal modes. The estimation was made based on the perturbation relationship, i.e., a sensitivity function was used to represent the change in formant frequency due to a small perturbation of the vocal-tract shape. Starting from initial values, the vocaltract parameters were optimized iteratively, and the sensitivity functions were used as linear constraints to update the parameter values. The estimation accuracy was examined using area function data for 10 English vowels (Story and Titze, J. Phon., 26, 223-260, 1998). The results showed that the method is capable of determining vocal-tract shape with a satisfactory degree of accuracy, though the estimation accuracy strongly depends on the type of vowel. The dependency of the estimation error on the initial values of the parameters was also investigated.