Dispersive Traveling Waves

In many acoustic systems, such as piano strings (§9.4.1,§C.6), wave propagation is also significantly dispersive. A wave-propagation medium is said to be dispersive if the speed of wave propagation is not the same at all frequencies. As a result, a propagating wave shape will ``disperse'' (change shape) as its various frequency components travel at different speeds. Dispersive propagation in one direction can be simulated using a delay line in series with a nonlinear phase filter, as indicated in Fig.2.5. If there is no damping, the filter $A(z)$ must be all-pass [452], i.e., $\vert A(e^{j\omega T})\vert=1$ for all $\omega T\in[-\pi,\pi]$ .

Figure 2.5: Dispersive traveling-wave simulator. In principle, the digital filter $A(z)$ provides an arbitrary nonnegative delay corresponding to one sample of wave propagation at each frequency.