STATIC AND DYNAMIC RELATIONS BETWEEN VOCAL TRACT CONFIGURATIONS

The relation between vocal tract configurations (VTC) and the acoustic signal represents a complicated non linear process. This phenomenon is inherently dynamic. In this article, aspects of this relation will be presented using a new speech production model, based on the Distinctive Regions and Mode (DRM) [8]. The parameters of the DRM model and its command strategy simplify and formalize the relation between the VTC and the acoustic parameters. The command inventory of the model is a set of dynamicaly defined gestures. In the acoustic domain formant transitions with time are formalized into a primitive lexicon which is related to the primitive gestures of the DRM model. Formant trajectories in the F1-F2-F3 space are also stylized and related to model gestures or combinations of gestures. l. LINKS IN VTC-ACOUSTICS Relations between variations in the vocal tract configurations A(x,t) and the output acoustic signal can deal with different parameters of this signal. Examples of acoustic parameters of the signal are: (l) formant frequencies Fn, (2) formant transitions in the time domain (FT), (3) formant bandwidth (Bn), (4) formant trajectories in the F1-F2-F3 space, (S) noise type, frequency, intensity and duration. One can trace-two main schools relating to the consideration of the variations of the VTCs. The first emphasises the articulatory aspect involved in the process, and consequently, concentrates on articulatory models and parameters and then relates the acoustic output to them. The second school emphasises the acoustic tube depicting the VTC, and as such concentrates on acoustic models and parameters taking into account physiological constraints. The DRM model is a model of the second school. It is not the object of this article to review literature on VTC-acoustic relations, nevertheless, it is helpful to mention some exemples of it. Chiba and kajiyama [4] related the increase or decrease in a resonant frequency of an acoustic tube to constricting the tube near the maximum point of the pressure standing wave, or near the maximum point of the volume velocoty respectivly. Perturbation theory has been successfully used to study the relation between a small area-function variation and a crresponding acoustic parameter variation [10]. Starting in 1967 Fant used this theory to develop the concept of Sensitivity Function. Sensitivity functions of an arbitrary area function A(x) relate, for a given formant, small local spatial perturbations to formant frequency or bandwidth. Sensitivity functions for length perturbations are also introduced by FANT and served as a measure of “formant-cavity” affiliations [6]. Sensitivity functions can also help to define formant stability as a function of local perturbations. The DRM model is based on the concept of sensitivity function. Several models of the vocal tract have been proposed to study the relation, between VTC and formant frequencies. These models are capable of providing insight into some area-function-acoustic relations or articulatory-acoustic relations. Fant [7] elaborated a model composed of four cavities representing the vocal tract. He provided nomograms relating the five formant frequencies to the dimensions of these four cavities. These nomograms