Estimating area function of the vocal tract from formants using a sensitivity function and least-squares

We present methods for estimating the cross-sectional area function of the vocal tract from formant frequencies. They extend the work of Story (J. Acoust. Soc. Am., 119, 715-718, 1996) based on a sensitivity function representing the change in the formant frequency due to a perturbation of the cross-sectional area. In Method I, the area function is estimated through an iterative procedure that uses the sensitivity function as the basis function to optimize the area function that produces the target frequencies. In Method II, a mode function linearly expands the area function. The estimation is performed by optimizing the value of each mode coefficient, where the sensitivity function is used as a constraint in the optimization. As a specific feature, the summing weight of sensitivity functions in Method I and mode functions in Method II is determined by minimizing an objective function representing the frequency error of every formant. By using existing area function data for English vowels, we compare the performance of each method with respect to the estimation accuracy and convergence speed. The results show that our methods can effectively reduce degrees of freedom of the area function and quickly obtain the optimal solution with fair accuracy.