For this study, we will explore digital waveguide techniques for achieving realistic conical bore instrument sounds.
A simple memory-less, non-linear reed function is used for the realtime implementations discussed here.
The reed-channel volume flow and pressure difference characteristic, shown in Fig. 12, is solved in terms of a non-linear traveling-wave reflection function (Smith, 1986) as:
pd is the pressure on the downstream side of the reed, pu is the player's breath pressure (upstream),
is the pressure difference across the reed, Zr is a time-varying reed ``impedance'', and Zo is the real wave impedance at the air column input.
Good results have been achieved using the simplified reed reflection function shown at the bottom of Fig. 12 in clarinet synthesis algorithms.
While the behavior of the reed function plays an important role in the overall quality of a synthesis model, the memory-less system is adequate for the purposes of evaluating the various air column models explored here.