Compact Green's functions extend the acoustic theory of speech production

Abstract

A brief tutorial discussion of the method of compact Green's functions applied to sources of sound in the vocal tract is given. A vocal tract transfer function may be regarded as a specialized Green's function. However, a Green's function enables detailed analysis of the transfer of energy from the hydrodynamic mode of fluid motion into sound. Source regions within the vocal tract often are small compared to the acoustic wavelength, which leads to a simplified model of the acoustics of the source region. This permits calculation of a ‘compact’ Green's function. In this approach much of the classical acoustic theory of speech production remains unchanged. The method is illustrated by the calculation of the sound source when a vortex is swept past an obstruction in the vocal tract. This is discussed in terms of the differences between the pressure sources of sibilant fricative production and of voicing and aspiration.