Dispersive Traveling-Wave Simulation

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

This is simulated using a filter having nonlinear phase.

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

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

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

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