Equivalence of finite difference approximation and digital waveguide modeling for lossless, nondispersive media in one to three dimensions

Abstract

The finite difference approximation method is commonly used to convert a differential equation into a recursive computation for computer simulation of an acoustic medium. Less well known is the digital waveguide modeling approach to the same problem, which is based on simulating the propagation of sampled traveling waves in the medium, and which implements losses and dispersion using digital filters applied to the traveling waves [Comput. Music. J., 74–91 (Winter 1992)]. It turns out the two methods are equivalent in rectilinear coordinates in one, two, and three dimensions, in the lossless, nondispersive case, provided the spatial sampling interval is chosen to be a specific constant (c in the one-dimensional case) times the temporal sampling interval. Since the digital waveguide simulation technique requires far less computational effort, it can be used to both accelerate and increase the accuracy of numerical simulations of acoustic media.