Mathematical Considerations in Digital Simulations of the Vocal Tract
Michael R. Portnoff, Ronald W. Schafer · The Journal of the Acoustical Society of America · 1973
The formulation of a digital simulation of speech production involves two basic steps. The first step is a mathematical representation of the physics of sound generation and propagation in the vocal tract. These processes are of a continuous nature and are generally represented mathematically by differential equations. The second step is the transformation of the mathematical description of the physical processes into a discrete-time model in the form of a set of difference equations suitable for implementation on a digital computer. As a result of this second step, a number of mathematical issues arise that are unrelated to the physics of speech production. These issues often receive insufficient consideration. In fact, it is easily shown that intuitively reasonable discrete-time approximations often have undesirable characteristics. The theory of digital signal processing provides a means for understanding these issues and for formulating accurate digital simulations. This approach is illustrated by a discussion of a simulation involving a soft-walled nonuniform acoustic tube excited by a two-mass model of the vocal cords.