Tuning of vocal tract model parameters for nasals using sensitivity functions

Determining the cross-sectional areas of the vocal tract models from the linear predictive coding or autoregressive-moving-average analysis of speech signals from vowels has been of research interest for several decades now. To tune the shape of the vocal tract to given sets of formant frequencies, iterative methods using sensitivity functions have been developed. In this paper, the idea of sensitivity functions is expanded to a three-tube model used in connection with nasals, and the energy-based sensitivity function is compared with a Jacobian-based sensitivity function for the branched-tube model. It is shown that the difference between both functions is negligible if the sensitivity is taken with respect to the formant frequency only. Results for an iterative tuning a three-tube vocal tract model based on the sensitivity functions for a nasal (/m/) are given. It is shown that besides the polar angle, the absolute value of the poles and zeros of the rational transfer function also needs to be considered in the tuning process. To test the effectiveness of the iterative solver, the steepest descent method is compared with the Gauss-Newton method. It is shown, that the Gauss-Newton method converges faster if a good starting value for the iteration is given.