Lutz Trautmann and Rudolf Rabenstein
University of Erlangen-Nuremberg

This paper describes the application of multidimensional system theory to string models for the simulation of acoustical instruments. It presents an extension from the solution of one-dimensional systems described by ordinary differential equations to multidimensional systems, described by partial differential equations. These systems describe time- and space-dependent physical phenomena. They are solved here with functional transformations to obtain a multidimensional transfer function model.

After inverse transformations and discretization of the transfer function model, this method leads to an efficient implementation algorithm for the simulation of the underlying partial differential equation. The example of a transversal vibrating string is used, but the technique is not restricted to digital sound synthesis; it can also be used for electro-magnetics, optics, acoustics, and heat and mass transfer.