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 having a known closed-form inverse could be useful in higher dimensions.

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written by 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.