A virtual model of spring reverberation

Abstract

The digital emulation of analog audio effects and synthesis components, through the simulation of lumped circuit components has seen a large amount of activity in recent years; electromechanical effects have seen rather less, primarily because they employ distributed mechanical components, which are not easily dealt with in a rigorous manner using typical audio processing constructs such as delay lines and digital filters. Spring reverberation is an example of such a system--a spring exhibits complex, highly dispersive behavior, including coupling between different types of wave propagation (longitudinal and transverse). Standard numerical techniques, such as finite difference schemes are a good match to such a problem, but require specialized design and analysis techniques in the context of audio processing. A model of helical spring vibration is introduced, along with a family of finite difference schemes suitable for time domain simulation. Various topics are covered, including numerical stability conditions, tuning of the scheme to the response of the model system, numerical boundary conditions and connection to an excitation and readout, implementation details, as well as computational requirements. Simulation results are presented, and full energy-based stability analysis appears in an Appendix.