Digital sound synthesis of string vibrations with physical and psychoacoustic models

The digital synthesis of musical sounds is a field with many applications in digital audio, computer music, and virtual environments. One family of sound synthesis methods is physical modeling, which is based on digital implementations of vibrating bodies. The physical model is expressed by partial differential equations which describe the dynamic behavior of strings, membranes, plates, and other resonators. Various methods can be used to convert a partial differential equation into a discrete- time model. The so-called functional transformation method expands the differential operators into their eigenfunctions and expresses the effect of each eigenfunction by a simple digital model. The numerical expense grows linearly with the number of considered eigenfunctions and can be quite large for 2D or 3D vibrating bodies. This contribution describes a method to reduce the number of basic digital models by considering only a representative subset of eigenfunctions. The selection of the eigenfunctions is based on the well-known concept of critical bands. Audio examples show that the number of relevant eigenfunctions can be considerably reduced without impairing the timbral quality of the synthesized sounds.