### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 5aMU8. Equivalence of finite difference approximation and digital
waveguide modeling for lossless, nondispersive media in one to three
dimensions.

**Julius O. Smith
**

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Scott A. Van Duyne
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**
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*Ctr. for Comput. Res. in Music and Acoust. CCRMA), Dept. of Music,
Stanford Univ., Stanford, CA 94305
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*
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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.