Digital Waveguides

A (lossless) digital waveguide is defined as a bidirectional delay line at some wave impedance $R$ [434,437]. Figure 2.11 illustrates one digital waveguide.

Figure 2.11: A digital waveguide $N$ samples long at wave-impedance $R$ .

As before, each delay line contains a sampled acoustic traveling wave. However, since we now have a bidirectional delay line, we have two traveling waves, one to the ``left'' and one to the ``right'', say. It has been known since 1747 [100] that the vibration of an ideal string can be described as the sum of two traveling waves going in opposite directions. (See Appendix C for a mathematical derivation of this important fact.) Thus, while a single delay line can model an acoustic plane wave, a bidirectional delay line (a digital waveguide) can model any one-dimensional linear acoustic system such as a violin string, clarinet bore, flute pipe, trumpet-valve pipe, or the like. Of course, in real acoustic strings and bores, the 1D waveguides exhibit some loss and dispersion^3.4 so that we will need some filtering in the waveguide to obtain an accurate physical model of such systems. The wave impedance $R$ (derived in Chapter 6) is needed for connecting digital waveguides to other physical simulations (such as another digital waveguide or finite-difference model).