Program to Compute Vocal-Tract Poles and Zeros
M. V. Mathews, P. Walker · The Journal of the Acoustical Society of America · 1962
A Fortran program is described for computing the poles and zeros of the vocal tract from its shape. The tract is represented as a set of cylindrical sections. Any number of sections may be used. One-dimensional wave propagation is assumed. The mouth and nose are approximated as spherical radiators. The glottis is represented as a volume-velocity source with infinite impedance. Three cases are treated: (1) a single tube excited at the glottis and radiating from the mouth; (2) a branched tube excited at the glottis with one branch for the mouth and one branch for the nose—either nose or mouth or both can radiate, (3) a single tube with excitation at the middle (corresponding to fricatives). The source can be represented either as a pressure- or volume-velocity source. The magnitude of the tract-transfer characteristic is computed as a function of frequency. The numerator and denominator of the transfer characteristic are also obtained separately to put the zeros and poles in evidence. The program is written in Fortran II and can be used on IBM 704, 709, and 7090 machines.