Summary

An explicit linear transformation was derived for converting state variables of the finite-difference time-domain (FDTD) scheme to those of the digital waveguide (DW) scheme. The equivalence of the FDTD and DW state transitions was reviewed, and the proof of state-space equivalence was completed. Since the DW scheme is exact within its bandwidth (being a sampled traveling-wave scheme instead of a finite difference scheme), it can be put forth as the proper physical interpretation of the FDTD scheme, and consequently be used to provide physically accurate initial conditions and excitations for the FDTD method. For its part, the FDTD method provides lower cost relative to the DW method in dimensions higher than one (for simulating membranes, volumes, and so on), and can be preferred in highly distributed nonlinear string simulation applications.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.