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 . 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.
Force-Pulse Filter Design