#### Digital Waveguide Single-Reed Implementation

A diagram of the basic clarinet model is shown in
Fig.9.39. The delay-lines carry left-going and
right-going *pressure* samples and (respectively) which
sample the traveling pressure-wave components within the bore.

The reflection filter at the right implements the bell or tone-hole
losses as well as the round-trip attenuation losses from traveling
back and forth in the bore. The bell output filter is highpass, and
*power complementary* with respect to the bell reflection filter
[500]. Power complementarity follows from the
assumption that the bell itself does not vibrate or otherwise absorb
sound. The bell is also *amplitude complementary*. As a result,
given a reflection filter designed to match measured mode
decay-rates in the bore, the transmission filter can be written down
simply as
for velocity waves, or
for pressure waves. It is easy to show that such
amplitude-complementary filters are also power complementary by
summing the transmitted and reflected power waves:

where denotes the *z* transform transform of the incident pressure wave,
and denotes the *z* transform of the incident volume-velocity. (All
*z* transform have omitted arguments
, where
denotes the sampling interval in seconds.)

At the far left is the reed mouthpiece controlled by *mouth
pressure* . Another control is *embouchure,* changed in
general by modifying the *reflection-coefficient* function
, where
. A simple choice of embouchure control is an
offset in the reed-table address. Since the main feature of the reed table
is the pressure-drop where the reed begins to open, a simple embouchure
offset can implement the effect of biting harder or softer on the reed, or
changing the reed stiffness.

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Scattering-Theoretic Formulation

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Force-Pulse Filter Design