Full Model

The nonlinear characteristic of the jet implies also that pressure waves impinging on the head termination actually reflect in a nonlinear fashion. We can adjust the model as shown in Figure 3 by inserting the nonlinear element $NL$ into the loop. $NL$ can be approximated using something similar to the soft-clipper combined with an extra delay line and an additional reflection [1]. In simplified terms, $NL$ essentially means that incoming pressure waves with large magnitudes are reflected with gains closer to 0 than -1.

Figure 3: Digital waveguide model of a flute