Single-matrix formulation of a time domain acoustic model of the vocal tract with side branches

Although it has been found that the piriform fossae play an important role in speech production and acoustics, the popular time domain articulatory synthesizer of [Maeda, S., 1982. A digital simulation method of the vocal-tract system. Speech Comm. 1 (3-4), 199-229] currently cannot include any more than one side branch to the acoustic tube that represents the main vocal tract. To overcome this limitation, in this paper we extended Maeda's (1982) simulation method, by mathematical reformulation in terms of a single-matrix equation having a system matrix that is both sparse and symmetric. Using vocal tract area functions measured by MRI, the simulation results showed that the piriform fossae suppress the energy in the higher frequencies by introducing spectral zeros around 4-5kHz, and also tend to lower the second formant of vowels. These spectral changes agree with results produced using a well-tested frequency domain transmission-line method, thus validating our new formulation of the time domain synthesizer. The reformulation can be easily extended to accommodate any number of vocal tract side branches, thus enabling more realistic, physiologically correct acoustic simulation of speech production.