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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

$\displaystyle y_{n,m-1}$ $\displaystyle =$ $\displaystyle y_{n,m-1} + u_{n-1}$  
$\displaystyle y_{n,m}$ $\displaystyle =$ $\displaystyle y_{n,m} + 2u_n$  
$\displaystyle y_{n,m+1}$ $\displaystyle =$ $\displaystyle y_{n,m+1} + u_{n-1}
\protect$ (E.23)

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 [224].


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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