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From 1D$ +$ to 1D$ \pm$

We have been modeling unidirectional traveling waves:

\epsfig{file=eps/wavesimfddel.eps,width=\textwidth }

\begin{eqnarray*}
\mbox{Attenuation per sample} &=& \vert H(e^{j\omega T})\vert\\ [10pt]
\mbox{Phase-shift per sample} &=& \angle H(e^{j\omega T})
\end{eqnarray*}

Thanks to superposition, we can simulate both directions of propagation in a 1D medium separately and add them only when needed:

\epsfig{file=eps/BidirectionalDelayLineSuperposition.eps,width=\textwidth }

(Lossless, Non-Dispersive Case)


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Download Delay.pdf
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``Computational Acoustic Modeling with Digital Delay'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2015-04-29 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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