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State Space Summary

We have seen that the DW and FDTD schemes correspond to state-space models which are related to each other by a simple change of coordinates (similarity transformation). It is well known that such systems exhibit the same transfer functions, have the same modes, and so on. In short, they are the same linear dynamic system. Differences may exist with respect to spatial locality of input signals, initial conditions, and boundary conditions.

State-space analysis was used to translate initial conditions and boundary conditions from one case to the other. Passive terminations in the DW paradigm were translated to passive terminations for the FDTD scheme, and FDTD excitations were translated to the DW case in order to interpret them physically.

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Download wgfdtd.pdf

``On the Equivalence of the Digital Waveguide and Finite Difference Time Domain Schemes'', by Julius O. Smith III, version published at (in PDF and PostScript formats only).
Copyright © 2005-12-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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