Speech Modelling Based on Acoustic-to-Articulatory Mapping

Some Notes on Nonlinearities of Speech

“…It consists in identifying, for a chosen vocal tract model constituted by a set of overlapping tubes, a set of parameters so that the resonances of the model correspond to the formants observed in a given produced speech sound. As is has been observed in [69], distinct vocal tract shapes can produce the same set of formant frequencies and therefore, a given set of formant values cannot univocally identify the vocal tract shape that has generated them (inverse problem). There are infinite solutions for the inverse problem.…”

“…This is done taking three aspects into account: a) the accuracy of the vocal tract shapes estimate via formant-toarea mapping in comparison to the real vocal shapes; b) the underlying vocal tract models used; c) the numerical stability. Results shown that a good approximation is guaranteed only for speech sounds that are produced with a simple vocal tract configuration "single cavity, single constriction, convex tongue, as well as constrained in the laryngo-pharynx, and, possibly, at the lips" [69]; models based on a small number of conical tubelets with continuously varying cross area sections are preferred to exponential tubelets and cylindrical tubelets; the convergence to the desired format frequency values could be obtained with a precision greater than 1 Hz, even though the estimated vocal tract shapes could quantitatively and qualitatively differ from those built via the observed formant frequencies.…”

“…Even when functional constraints are imposed (such as minimal deformation, or minimal deformation rate of the vocal tract about a reference shape, or minimal deformation jerk) the inverse mapping does not fix the model, i.e., the real vocal tract shape that has produced that sound. To highlight the problems involved in the implementation of the acoustic-to-articulatory mapping, Schoentgen [69] reports a series of experiments where formant frequencies measured from sustained American English sounds are used to identify the corresponding vocal tract shapes. This is done taking three aspects into account: a) the accuracy of the vocal tract shapes estimate via formant-toarea mapping in comparison to the real vocal shapes; b) the underlying vocal tract models used; c) the numerical stability.…”