A study of ambiguities in the acoustic-articulatory mapping
Bishnu Saroop Atal · The Journal of the Acoustical Society of America · 2007
At Bell Laboratories, in 1976, Max Mathews, John Tukey, J. J. Chang, and I investigated the relationship between the shape of the vocal tract and its acoustic output for studying articulatory compensation. Although the mathematics of the forward transformation, from the vocal-tract shape to its acoustics, is reasonably clear, the same cannot be said about the inverse transformation from acoustics to the corresponding vocal-tract shape. Max, recognizing the increasing power of digital computers, suggested an interesting approach to the inverse problem, based on computer-sorting. Inversion by computer-sorting consisted of computing the output for many values of the input and sorting the resulting output-input pairs into a convenient order, according to the output data. The paper will highlight this approach and present some interesting results of this study on articulatory compensation. We were successful in determining articulatory regions (fibers) that map into a single point in the acoustic space and produce the same sound [Atal et al., J. Acoust. Soc. Am. 63, 1535–1555 (1978)].