Next  |  Prev  |  Up  |  Top  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Digital Waveguide Models

A more efficient alternative to the finite-difference approximation, when it applies, is the so-called ``digital waveguide approach'' [153,162]. Its characteristics are well matched to the problem of real-time string simulation. Instead of digitizing the differential equation for the string, digital waveguide models modify the solution of the ideal wave equation by introducing digital filters which simulate amplitude attenuation and phase dispersion [156]. This two-step procedure yields finite difference schemes which are orders of magnitude less expensive computationally, relative to FDAs, without sacrificing sound quality in the acoustic simulation [157]. Since the variables in the resulting model retain precise physical interpretations, nonlinearities and time-varying parameters can be implemented in the same way as in the FDA method. Furthermore, FDAs and digital waveguides can be freely intermixed [86,87,96,119,120]. The digital waveguide approach is most effective for modeling physical systems that support traveling waves and for which losses, dispersion, and any nonlinearities can be well modeled psychoacoustically at spatially localized points. Fortunately, many acoustic musical instruments fit this description, including strings, winds, brasses, and tonal percussion.

As a general rule, linear elements consisting of uniform mass distributions primarily along one dimension, such as vibrating strings, woodwind bores, pipes, horns, and the like, are most efficiently modeled using the digital waveguide framework. (From a modal synthesis point of view, digital waveguides are highly efficient for simulating large numbers of quasi-harmonic resonances.) On the other hand, systems which are nonlinear, or which have only one important resonance (or anti-resonance) in the band of human hearing such as clarinet reeds, toneholes, lip valves, and piano hammers, are generally better modeled using the FDA approach. Other situations arise as well, some of which will be noted below.


Next  |  Prev  |  Up  |  Top  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Download jnmr.pdf

``Virtual Acoustic Musical Instruments: Review and Update'', by Julius O. Smith III, DRAFT to be submitted to the Journal of New Music Research, special issue for the Stockholm Musical Acoustics Conference (SMAC-03) .
Copyright © 2005-12-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  [Automatic-links disclaimer]