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Dispersive Traveling-Wave Simulation

In many acoustic systems, such as piano strings, wave propagation is also dispersive.

\begin{figure}\centering \input fig/wavesimfddel.pstex_t \\ {\LARGE } \end{figure}

This is simulated using a filter having nonlinear phase.

For lossless, dispersive wave propagation, the filter is ``allpass,'' i.e.,

$\displaystyle \left\vert H(e^{j\omega T})\right\vert \equiv 1, \;\forall \omega $

Note that a delay line is a special case of an allpass filter:

$\displaystyle \left\vert e^{j\omega MT}\right\vert \equiv 1, \;\forall \omega $

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``Computational Acoustic Modeling with Digital Delay'', 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