Tuning of vocal tract model parameters for nasals using sensitivity functions

Abstract

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.

A morphological and acoustic analysis of the vocal tract during the act of whistling

“…Consequently, these functions are flexible, and capable of treating any type of resonance, or even anti-resonance. Kreuzer and Kasess [20] also reported that a complex sensitivity function for formants was largely in accord with traditional, physically-derived sensitivity functions.…”

“…To perform sensitivity analysis, a sensitivity function must be newly derived with regard to the peaks of input impedance, because previously reported sensitivity functions [16,17] are related to peaks of the vocal-tract transfer function. To derive a sensitivity function, we used the basic concept of a complex sensitivity function [20]. Unlike the existing sensitivity functions derived from a physical principle [15], complex sensitivity functions are derived formally.…”

“…However, these sensitivity functions did not fit the current experimental paradigm, because the vocal-tract resonance was determined for whistling as the peak of the input impedance. We therefore computed the perturbation relationship on the basis of a complex sensitivity function [20]. Using this sensitivity analysis, we demonstrated that the anterior cavity of the vocal tract was more sensitive than the posterior cavity to the frequency of an impedance peak.…”

An acoustically-driven vocal tract model for stop consonant production

“…It can be noted that an alternative to the energy-based approach is to calculate the sensitivity functions with a Jacobian formulation (Kreuzer & Kasess, 2015). The advantage is that both the frequency and bandwidth of each vocal tract resonance enter into the calculation which may be particularly useful for enhancing modification of tract configurations that include branching into the nasal passages or subglottal airways.…”

“…Carré’s work focused on how perturbations of a uniform tubular conduit seem to give rise to the vocal tract shapes observed in speech articulation, whereas the goal in Story (2006) was in tuning measured vocal tract shapes such that their calculated resonance frequencies better matched the formant frequencies obtained from analysis of recorded speech. Adachi et al (2007) and Kreuzer and Kasess (2015) formulated a similar iterative approaches but added the effects of vocal tract length perturbation and nasal branching, respectively, to the calculation of acoustic sensitivity functions.…”