Extension of the single-matrix formulation of the vocal tract: Consideration of bilateral channels and connection of self-oscillating models of the vocal folds with a glottal chink

The paper presents extensions of the single-matrix formulation (Mokhtari et al., 2008, Speech Comm. 50(3) 179 - 190) that enable self-oscillation models of vocal folds, including glottal chink, to be connected to the vocal tract. They also integrate the case of a local division of the main air path into two lateral channels, as it may occur during the production of lateral consonants. Provided extensions are detailed by a reformulation of the acoustic conditions at the glottis, and at the upstream and downstream connections of bilateral channels. The simulation framework is validated through numerical simulations. The introduction of an antiresonance in the transfer function due to the presence of asymmetric bilateral channels is confirmed by the simulations. The frequency of the antiresonance agrees with the theoretical predictions. Simulations of static vowels reveal that the behavior of the vocal folds is qualitatively similar whether they are connected to the single-matrix formulation or to the classic reflection-type line analog model. Finally, the acoustic effect of the glottal chink on the production of vowels is highlighted by the simulations: the shortening of the vibrating part of the vocal folds lowers the amplitude of the glottal flow, and therefore lowers the global acoustic level radiated at the lips. It also introduces an offset in the glottal flow waveform.