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Sampled Traveling-Wave Solution

As discussed in more detail in Appendix C, the continuous traveling-wave solution to the wave equation given in Eq.$ \,$ (6.2) can be sampled to yield

$\displaystyle y(nT,mX)$ $\displaystyle =$ $\displaystyle y_r(nT-mX/c) + y_l(nT+mX/c)$   $\displaystyle \mbox{(set $X=cT$)}$  
  $\displaystyle =$ $\displaystyle y_r(nT-mT) + y_l(nT+mT)$  
  $\displaystyle \isdef$ $\displaystyle y^{+}(n-m) + y^{-}(n+m)
\protect,$ (7.3)

where $ T$ denotes the time sampling interval in seconds, $ X=cT$ denotes the spatial sampling interval in meters, and $ y^{+}$ and $ y^{-}$ are defined for notational convenience.


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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
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