Digital Sound Synthesis Based on Transfer Function Models

Various methods for sound synthesis based on physical models have been presented. They start from a continuous model for the vibrating body, given by partial differential equations (PDEs), and employ proper discretization in time and space. Examples are wave guide models or finite difference models. A different approach is presented here. It is based on a multidimensional transfer function model derived by suitable functional transformations in time and space. Physical effects modeled by the PDE like longitudinal and transversal oscillations, loss and dispersion are treated with this method in an exact fashion. Moreover, the transfer function models explicitely take initial and boundary conditions, as well as excitation functions into account. The discretization based on analog-to-discrete transformations preserves not only the inherent physical stability, but also the natural frequencies of the oscillating body. The resulting algorithms are suitable for real-time implementation on digital signal processors. This paper shows the new method on the linear example of a transversal oscillating tightened string with frequency dependent loss terms.