Subject: Re: A question on area function of vocal tract From: Steve Beet <steve.beet@xxxxxxxx> Date: Wed, 30 Aug 2006 20:57:28 +0100Xinhui, Jont, Dick, et al. Another important effect which is often neglected in vocal tract modelling is the variation in the sound velocity as a function of frequency within a fleshy tube! This is due to both higher propagation modes (from around 4kHz and above) and to the elasticity of the vocal tract (which has most effect just above 100 Hz). I described a preliminary investigation of these effects in my PhD thesis - "Digital Processing of Speech Produced in Hyperbaric Helium", S W Beet, University of Liverpool (UK), 1985 (unfortunately before the days of online publishing, PDF files and almost everything else). Also unfortunately, I never took this work any further or published it in any more detail. But the up-shot was that the effective speed of sound propagation within an idealised vocal tract (and hence the frequency of its resonances) suffers two discontinuities within the typical speech signal bandwidth. One near 100Hz, and another just above 4kHz. This idealised, but elastic-walled, vocal tract model matched up pretty well with actual measurements of vocal tract impedance (Wheeler, Elliott and Darlington, ISVR, 1984), except that the observed discontinuity which should have appeared around 4kHz was actually observed closer to 3kHz. It may be that this was because of the shape of the vocal tract (my model assumed it was linear), or it may just be because I got some of the model's parameters wrong. Steve Beet