Vocal tract area functions from two point acoustic measurements with formant frequency constraints

Abstract

A formulation is presented by which the cross-sectional areas of the vocal tract can be computed from the pressure spectrum. The pressure spectrum is the magnitude squared of the transfer function relating acoustic pressure at the glottis to pressure measured in the acoustic radiation field beyond the lips. Two correction parameters are determined using an iterative procedure. One parameter relates to the absolute scaling of the vocal tract areas; the other parameter is the area of the vocal tract at its driving point. This formulation is not robust when applied to a vocal tract with wall losses. The problem results from the effect of wall losses on the amplitudes of pressure spectrum peaks. A correction factor is applied which constrains the formant frequencies of the estimated vocal tract shape to match observed formant frequencies. This correction factor is obtained by a noniterative procedure. The resulting area function estimation procedure is applied to acoustic data computed from the Fant area functions. The area function estimates show the procedure to be robust in the case of lossy vocal tract walls and a free space radiation load.