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

Abstract

We present numerical methods for studying the relationship between the shape of the vocal tract and its acoustic output. For a stationary vocal tract, the articulatory-acoustic relationship can 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, we develop a procedure for inverting f(x). Inversion by computer sorting consists 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 is 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 is presented. A method is also described for finding articulatory regions (fibers) which map into a single point in the acoustic space. The local nature of f(x) is determined by linearization in a small neighborhood. Larger regions are 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 show that, in many cases of interest, a given sound could be produced by many different vocal-tract shapes.

Invariance and variability in the production of the height feature in French vowels

“…Because of the many-to-one relationship between articulatory configurations and acoustic values (e.g., Atal et al, 1978;Boë et al, 1992), an iterative procedure incorporating random search was carried out to retrieve over 50 possible articulatory configurations for each vowel, for a given growth stage. All of these configurations produce exactly the same formants, providing a sample of different articulatory configurations compatible with the acoustic output.…”

Dynamic action units slip in speech production errors

“…simply reflect non-errorful variation in the levels of co-contracting muscles. Also, acoustic investigations of speech errors do not allow for an unambiguous interpretation of the articulatory events that have rendered a particular acoustic outcome, due to the complex relationship between acoustics and articulations (Atal, Chang, Mathews, & Tukey, 1978;Chen, 2003).…”

A method for finding constrictions in high front vowels

“…Utilizing these constraints on the value of k, it turns out that the plateau of high F 2 values crosses the k = 3 line at n Ͼ 2. However, since the acoustic-to-articulatory mapping itself is well-known to be indeterminate (Atal et al, 1978), it should not be surprising that constraints on the values of F 1 , F 2 , and F 3 are not sufficient to uniquely determine the parameters of the procedure for finding the constriction in a given x-ray profile.…”