Digital sound synthesis by physical modelling

After recent advances in coding of natural speech and audio signals, the synthetic creation of musical sounds is also gaining importance. Various methods for waveform synthesis are currently used in digital instruments and software synthesizers. A family of new synthesis methods is based on physical models of vibrating structures (string, drum etc.) rather than on descriptions of the resulting waveforms. This article describes various approaches to digital sound synthesis in general and discusses physical modelling methods in particular. Physical models in the form of partial differential equations are presented. Then it is shown, how to derive discrete-time models which are suitable for real-time DSP implementation. Applications to computer music are given as examples.