A digital simulation method of the vocal-tract system

Abstract

A time-domain simulation method of the vocal-tract system is described. The system, composed of a constant air pressure source, a time-varying narrow section representing the glottis and a tube corresponding to the vocal tract coupled with the nasal cavity was assumed as a vocal-tract model. The acoustic equations that govern the generation and the propagation of acoustic waves inside the model were transformed into the discrete variable representation by applying certain rules; the rectangular rule in space and the trapezoid rule in time. This particular manner of discretization causes spectral distortion due to the frequency warping. A theoretical analysis indicated that this warping can be interpreted as the manifestation of the frequency dependent phase velocity of waves in the discrete system. The magnitude of the warping depends on both the sampling frequency ( f s) and the sampling interval in space ( X). Eleven French vowels synthesized with f s = 20 kHz and X = 1 cm sounded very natural and highly intelligible, even though a trace of the frequency warping was noticeable at the third formant frequency region on their spectra. When f s = 40 kHz was used, the effect of the spectral distortion became practically negligible for frequencies below 4 kHz.