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Future Work

The simple state translation formulas derived here for the one-dimensional case do not extend simply to higher dimensions. While straightforward extensions to higher dimensions are presumed to exist, a simple and intuitive result such as found here for the 1D case could be more useful for initializing and driving FDTD mesh simulations from a physical point of view. In particular, spatially localized initial conditions and boundary conditions in the DW framework should map to localized counterparts in the FDTD scheme. A generalization of the Toeplitz operator $ \mathbf{T}$ having a known closed-form inverse could be useful in higher dimensions.


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA