Numerical inversion of the transformation from articulatory to acoustic parameters in the vocal tract

Abstract

A method is presented for determining the parameters of an articulatory model corresponding to a given set of formant frequencies. A four-parameter articulatory model of the vocal tract was used to define the vocal-tract shape. The articulatory parameters were (a) location of constriction, (b) area of constriction, (c) area of mouth opening, and (d) length of the vocal tract. The model included losses due to finite wall impedance, glottal leakage, friction, heat conduction and radiation. Frequencies, amplitudes, and bandwidths of five formants were computed for each of 30 720 vocal-tract shapes obtained by uniform sampling along each of the four articulatory dimensions. The data was sorted according to the first three formant frequencies. The articulator positions yielding given values of these formant frequencies can be looked up in the sorted data. One-dimensional fibers (curved lines) were computed along which the articulator positions can vary without producing changes in the three formant frequencies. These fibers span large distances in the articulatory space. Sounds produced by various articulations along a fiber were computed and were compared by informal listening tests.