Time-domain model of the singing voice
A combined physical model for the human vocal folds and vocal tract is presented. The vocal fold model is based on a symmetrical 16 mass model by Titze. Each vocal fold is modeled with 8 masses that represent the mucosal membrane coupled by non-linear springs to another 8 masses for the vocalis muscle together with the ligament. Iteratively, the value of the glottal flow is calculated and taken as input for calculation of the aerodynamic forces. Together with the spring forces and damping forces they yield the new positions of the masses that are then used for the calculation of a new glottal flow value. The vocal tract model consists of a number of uniform cylinders of fixed length. At each discontinuity incident, reflected and transmitted waves are calculated including damping. Assuming a linear system, the pressure signal generated by the vocal fold model is either convoluted with the Green’s function calculated by the vocal tract model or calculated interactively assuming variable reflection coefficients for the glottis and the vocal tract during phonation. The algorithms aim at real-time performance and are implemented in MATLAB.