We present a method to simultaneously estimate the cross-sectional area and length of the vocal tract from a speech spectrum. An iterative procedure determines the vocal-tract shape by gradually optimizing the parameter values to produce the target speech spectrum. The vocal-tract shape is updated in each iteration using a sensitivity function representing the change in formant frequency caused by a slight perturbation of the vocal-tract shape. Our method effectively optimizes the vocal-tract shape when combined with the perturbation relationship between the speech spectrum parameters (i.e., cepstral parameters) and formants. The estimation accuracy is examined using area function data for 10 English vowels (Story and Titze, J. Phon., 26, 223-260, 1998). The resulting average errors are 0.36 cm2 for the cross-sectional area and 0.21 cm for the vocal-tract length. This corresponds to a 17.6% and 1.24% error, respectively. The formant frequency recovered from the estimated vocal-tract shape has an error of less than 4% for each of the first four formants. We also determine that the fundamental frequency of the target speech spectrum has an influence on the estimation accuracy.
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