Padé approximations for boundary-layer losses in articulatory synthesis

Abstract

To build an articulatory synthesizer it is necessary to model acoustic propagation in tubes with variable area. Acoustic propagation entails viscous and thermal losses, which are strongest at the vocal tract walls. In the standard boundary-layer approximation irrational frequency laws containing the square root of frequency best represent these losses. Our immediate goal is, given a sound source distribution in the vocal tract, to efficiently calculate the sound output from the mouth. In order to use digital filter theory in this process, a rational approximation to the square root of frequency is sought in the form of Padé approximations. One implementation is obtained by modification of the Kelly–Lochbaum algorithm for calculating wave propagation in a tube, using a high over-sampling rate. However, frequency-dependent loss means that both the reflection coefficients and the time delays through a tube section are non-constant functions of frequency—an assumption used in the Kelly–Lochbaum algorithm. The reflection coefficients are replaced by digital filters and the delay elements by filters with frequency-dependent group velocities. We discuss implementation of a Kelly–Lochbaum algorithm in a digital filter design using a Padé approximation of the viscous and thermal loss terms. [Work supported by NIH Grant No. DC-01247.]