This is the reference article used for the acoustic model implemented in the software.
The sound field inside interconnected acoustic ducts with varying cross-section is modelled with a variational formulation of the Webster equation. The Sondhi model is used to take wall admitance and visto-thermal effects into account. The acoustic network of interconnected ducts is represented by a graph where each edge represents a duct described by a one-dimensional area function. We develop here numerical methods that allow us to solve the Webster equation in Laplace transform domain and to compute the transfer function between two given points of the acoustic graph. Resonances are obtained as eigenvalues of a matrix build with the area functions of the entire graph. Graph algorithms are used to identify subgraphs responsible for anti-resonances (zeros) of the transfer function. First, subgraphs that can be disconnected from any path joining input and output and that behave like Helmoltz resonators. Then we point out that subgraphs that contains cycles are also responsible for zeros in the transfer function. The first ones (disconnected) can, as the poles, be obtained by computing the eigenvalues of a matrix build with the area functions of the subgraph. The second ones (cycle) require more numerical analysis in order to be computed from the transfer function for being used in discrete time signal processing. Afterwards, we present experimental measurements that validate the results of our computations. We conclude by a discussion on the most appropriated numerical schemes for modelling acoustic properties of ducts that contains sharp constrictions.
This is the reference article used for the glottal wave model implemented in the software.
Here we present the numerical method used for generating LF glottal flow. The computation time for calculating one LF glottal cycle does not exceeds 2 10-4 sec on an Intel core i7 processor running at 4.7 GHz. This makes it almost suitable for real-time articulatory speech synthesis.
The Acoustic Model used to take into account thermal and viscosity effects as well as wall admitance in to account is
Sondhi,M M, Model for wave propagation in a lossy vocal tract. Journal of the Acoustical Society of America, pages 1070-1075, Vol 55, 1974
The reference paper used for generating the Glotal Wave Signal is
Fant, Gunar, THE VOICE SOURCE. MODELS AND PERFORMANCE. Proceedings ICPhS 95 Stockholm pages 82-89 Vol 3, 1995
This is the article from which area function are extracted for this example
Story, B H and Titze, I R and Hoffman, E A, Vocal tract area functions from magnetic resonance imaging, JASA, 1996, Vol 100, pp 537-554
This external multirate notes from Phil Schniter (p 13) is the reference used for the reampling algorithm implementattion.