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Sampled Traveling Waves in any Digital Waveguide

\begin{displaymath}
\begin{array}{rclcl}
x &\to& \xm &=& mX\nonumber \\
t &\to& t_n&=& nT\nonumber
\end{array}\end{displaymath}

$ \Rightarrow$

\begin{eqnarray*}
y(t_n,\xm ) &\,\mathrel{\mathop=}\,& y_r(t_n- \xm /c) + y_l(t...
... \\
&\,\mathrel{\mathop=}\,& y^{+}(n-m) + y^{-}(n+m) \nonumber
\end{eqnarray*}

where we defined

$\displaystyle y^{+}(n) \mathrel{\stackrel{\Delta}{=}}y_r(nT) \qquad\qquad y^{-}(n) \mathrel{\stackrel{\Delta}{=}}y_l(nT)
$



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``Distributed Modeling in Discrete Time'', by Julius O. Smith III and Nelson Lee,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-06-05 under the Creative Commons License (Attribution 2.5), by Julius O. Smith III and Nelson Lee
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA