INTERSPEECH 2004 - ICSLP
A time domain simulation of acoustic propagation in the vocal tract requires the spatial and temporal discretization of the equations of motion and continuity. In the classic transmission line model of the vocal tract with lumped elements, the spatial discretization is provided by the piece-wise constant area function. The temporal finite-difference approximation of the differential equations can, however, vary from one implementation to the other. In this study, we have adopted a general finite-difference scheme that depends on a parameter t where 0 <= t <= 1. As special cases, this general method includes the trapezoid rule (t=0.5) as well as the implicit (t=1) and explicit (t=0) finite-difference schemes. We have examined how formant frequencies and bandwidths of simulated vowels are effected by the choice of t. The experiments were conducted for the sampling rates of 44.1 kHz and 88.2 kHz and compared with the accurate and thus desirable frequencies and bandwidths measured in frequency domain simulations of the vocal tract. It can be shown that optimal values for t are slightly above 0.5 depending on the sampling rate.
Bibliographic reference. Birkholz, Peter / Jackel, Dietmar (2004): "Influence of temporal discretization schemes on formant frequencies and bandwidths in time domain simulations of the vocal tract system", In INTERSPEECH-2004, 1125-1128.