Summary: Modeling the fiansitory Behavior of Speech Using a Time-varying Transmission-line Model
Amit S. Rane, Derrick C. Wei, Lisa E, Falkson, and Abeer A. Alwan
Speecl~ Processing and Auditoy Perception hborato~
Department of Electrical Engineering, University of Calfornia hs Angeles, hs Angeles, CA 90095.
Abstract: In this study, a transmission-line model of speech production (1) is modified so that changes in the vocal-tract
~ area functions, reflecting changes in the VT shape from one sound to another, are properly modeled. Each ~ shape is
divided into uniform cylindrical sections and each section is modeled by its equivalent transmission line comprising Resis-
tors (R), Capacitors (C), and Inductors (L). A radiation impedance terminates the transmission-line sections. For voiced
sounds, the ~SYN88 glottal waveform (2) is used as input. The model is simulated in time and frequency by using the ana-
Iog-circuit simulator HSPICE. To simulate the transitory characteristics of speech, different interpolations such as linear,
cubic and Fourier Transform are used for area transitions. The interpolated values result in a `sampled' area function and the
elements of each section are varied according to these time-sampled values. These variations are accomplished by utiIizing
time-varying independent voltage sources, ExampIes using American English dipthongs will be presented. Forrnant frequen-
cies (both steady-state and transitions) of the synthesized and natural dipthongs are in close agreement.
The vocal tract can be modeled as a concatenation of uniform cylindticaI-tube sections where each section is approximated as a
lumped circuit. Figure 1 shows a lumped circuit approximation for one section of the vocal tract; the values of the components (R,
L, C, and G) are from (3). This approximation is valid as long as the cross dimensions are small when compared to the wavelength
of the sound produced, For most configurations, the approximation is valid up to about 4-5 kHz.