The purpose of this study was to further develop a multi-tier model of the vocal tract area function in which the modulations of shape to produce speech are generated by the product of a vowel substrate and a consonant superposition function. The new approach consists of specifying input parameters for a target consonant as a set of directional changes in the resonance frequencies of the vowel substrate. Using calculations of acoustic sensitivity functions, these "resonance deflection patterns" are transformed into time-varying deformations of the vocal tract shape without any direct specification of location or extent of the consonant constriction along the vocal tract. The configuration of the constrictions and expansions that are generated by this process were shown to be physiologically-realistic and produce speech sounds that are easily identifiable as the target consonants. This model is a useful enhancement for area function-based synthesis and can serve as a tool for understanding how the vocal tract is shaped by a talker during speech production. (C) 2016 Elsevier B.V. All rights reserved.

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The traditional way of estimating the formant frequencies from articulatory data presupposes knowledge of how the vocal tract cross-sectional area varies for a given articulatory shape (Fant 1960/1970). Accordingly, in order to derive the formant pattern of a given articulation, the three-dimensional shape of the vocal tract (VT) needs to be known. In the past cross-sectional areas have typically been derived by means of ‘d-to-A rules’ that use the mid-sagittal cross-distance d at each point along the VT to produce a corresponding cross-sectional area A. X-ray and MRI data have been used to calibrate such rules (Heinz & Stevens 1964, Sundberg et al. 1987, Ericsdotter 2005). Although this procedure has produced many useful results it is time consuming and laborious. It is speaker-specific. It presupposes access to information on the three-dimensional shape of the VT, which is not experimentally readily accessible. Such observations raise the question whether sufficiently accurate alternative approaches can be developed. Is it possible to go straight from articulatory data to formant frequencies without having to construct a cross-sectional area function? If such methods could be developed it would have many uses both in phonetics and practical applications. This paper reports an attempt to map the time variations of selected articulatory parameters from X-ray profiles directly on the formant tracks using multiple regression analysis. Preliminary results for F1 indicate that multiple regression analysis can indeed be useful for making such predictions. The prospects of extending the present analyses to other formants are discussed.