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Additive Inputs

Instead of initial conditions, ongoing input signals can be defined analogously. For example, feeding an input signal $ u_n$ into the FDTD via

$\displaystyle y_{n,m-1}$ $\displaystyle =$ $\displaystyle y_{n,m-1} + u_{n-1}$  
$\displaystyle y_{n,m}$ $\displaystyle =$ $\displaystyle y_{n,m} + 2u_n$  
$\displaystyle y_{n,m+1}$ $\displaystyle =$ $\displaystyle y_{n,m+1} + u_{n-1} \protect$ (24)

corresponds to physically driving a single sample of string displacement at position $ m$. This is the spatially distributed alternative to the temporally distributed solution of feeding an input to a single displacement sample via the filter $ H(z)=1-z^{-2}$ as discussed in [13].

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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 http://arXiv.org/abs/physics/0407032 (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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