Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique

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Abstract
Numerical methods were presented for studying the relationship between the shape of the vocal tract [human] and its acoustic output. For a stationary vocal tract, the articulatory-acoustic relationship could be represented as a multidimensional function of a multidimensional argument: y = f(x), where x, y are vectors describing the vocal-tract shape and the resulting acoustic output, respectively. Assuming that y may be computed for any x, a procedure was developed for inverting f(x). Inversion by computer sorting consisted of computing y for many values of x and sorting the resulting (y, x) pairs into a convenient order according to y; x for a given y was then obtained by looking up y in the sorted data. Application of this method for determining parameters of an articulatory model corresponding to a given set of formant frequencies was presented. A method was also described for finding articulatory regions (fibers) which map into a single point in the acoustic space. The local nature of f(x) was determined by linearization in a small neighborhood. Larger regions were explored by extending the linear neighborhoods in small steps. This method was applied for the study of compensatory articulation. Sounds produced by various articulations along a fiber were synthesized and were compared by informal listening tests. These tests showed that, in many cases of interest, a given should could be produced by many different vocal-tract shapes.
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