Re: A question on area function of vocal tract

[Steve Beet <steve.beet@xxxxxxxx>]

Xinhui, 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