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Digital Waveguide Models
In this chapter, we summarize the basic principles of digital
waveguide models. Such models are used for efficient synthesis of
string and wind musical instruments (and tonal percussion, etc.), as
well as for artificial reverberation. They can be further used in
modal synthesis by efficiently implementing a quasi harmonic series of
modes in a single ``filtered delay loop''.
We begin with the simplest case of the infinitely long ideal vibrating
string, and the model is unified with that of acoustic tubes. The
resulting computational model turns out to be a simple
bidirectional delay line. Next we consider what happens when a
finite length of ideal string (or acoustic tube) is rigidly terminated
on both ends, obtaining a delay-line loop. The delay-line loop
provides a basic digital-waveguide synthesis model for (highly
idealized) stringed and wind musical instruments. Next we study the
simplest possible excitation for a digital waveguide string model,
which is to move one of its (otherwise rigid) terminations.
Excitation from ``initial conditions'' is then discussed, including
the ideal plucked and struck string. Next we introduce damping
into the digital waveguide, which is necessary to model realistic
losses during vibration. This much modeling yields musically useful
results. Another linear phenomenon we need to model, especially for
piano strings, is dispersion, so that is taken up next.
Following that, we consider general excitation of a string or tube
model at any point along its length. Methods for calibrating models
from recorded data are outlined, followed by modeling of coupled
waveguides, and simple memoryless nonlinearities are introduced and
analyzed.
Subsections
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