A passive nonlinear digital filter design which facilitates physics-based sound synthesis of highly nonlinear musical instruments

Abstract

Nonlinearities, small or large, favorably affect the sounds of many musical instruments. In gongs and cymbals, nonlinearities cause the passive transfer of energy from lower frequency modes to higher frequency modes after the instrument has been struck. While many spectral modifications can be achieved by the inclusion of memoryless nonlinearities (such as square-law or table look-up) within the resonant loops of physics-based digital sound synthesis algorithms, energy conservation cannot be achieved without compensating amplitude scaling. In fact, the greater the nonlinear effect desired, the more difficult it is to maintain passivity. Yet, for gongs and cymbals, a very large nonlinear effect is required. A computationally efficient nonlinear digital filter has been designed based on a physical system constructed from passive lossless elements only. This filter may be incorporated into any physical modeling algorithm (such as Karplus–Strong, digital waveguide, or 2D digital waveguide mesh) where traveling waves are being computed. System loss is decoupled from the nonlinear effect, and may be designed independently. Further, system energy spreads locally in the spectrum, as is found in real musical instruments; the rate and spectral region of energy spreading is controllable. Promising gong sounds have been produced.