Digital Waveguides

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

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*
(derived in Chapter 6) is
needed for connecting digital waveguides to other physical simulations
(such as another digital waveguide or finite-difference model).

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University