Transfer function models with nonlinear excitations for digital sound synthesis

Transfer functions for digital sound synthesis based on physical models have recently been presented. The method transforms a continuous model for the vibrating body, given by a partial differential equation (PDE), into a multidimensional transfer function model (TFM). The TFM not only takes initial and boundary conditions, as well as excitation functions into account, but also treats the physical effects modeled by the PDE exactly. The algorithms obtained after discretization of the TFM preserve the inherent physical stability and are suitable for real-time implementations on digital signal processors. A recently presented example of a linear transversal oscillating tightened string with frequency dependent loss terms is extended here by nonlinear excitations. They are modeled from real bow-string and hammer-string interactions in violins and pianos.