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Physical Audio Signal Processing
    Equivalence of Digital Waveguide and Finite Difference Schemes
       Excitation Examples
          Additive Inputs

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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

$\displaystyle y_{n,m-1}$ $\displaystyle =$ $\displaystyle y_{n,m-1} + u_{n-1}$  
$\displaystyle y_{n,m}$ $\displaystyle =$ $\displaystyle y_{n,m} + 2u_n$  
$\displaystyle y_{n,m+1}$ $\displaystyle =$ $\displaystyle y_{n,m+1} + u_{n-1} \protect$ (P.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 [227].

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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.


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