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Impulsive Signals Interpretation

Let $c$ denote the speed of propagation in one branch of an $m$-variable waveguide section having real, positive wave impedance ${\mbox{\boldmath$R$}}$. Let $L$ be the linear length of this branch in samples. The propagation time from one end to the other is $T_p = L /
c$. If $T_p = n T$, where $T$ is the sampling interval of the digital network, the (frequency-independent) propagation in the branch can be precisely simulated (ignoring any roundoff errors due to scattering at the endpoints). Extending this restriction to every branch in the network, we can state that a DWN is equivalent to a physical waveguide network in which the input pressure signals are streams of weighted impulses at intervals of $T$ seconds. This equivalence is also true in the case of time-varying wave impedances. The impulsive nature of the propagating signals serves to sample the junction scattering coefficients at the digital sampling instants.


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Download wgj.pdf

``Aspects of Digital Waveguide Networks for Acoustic Modeling Applications'', by Julius O. Smith III and Davide Rocchesso , December 19, 1997, Web published at http://ccrma.stanford.edu/~jos/wgj/.
Copyright © 2007-02-07 by Julius O. Smith III and Davide Rocchesso
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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