The Wave Digital Reed: a Passive Formulation

In this short paper, we address the numerical simulation of the single reed excitation mechanism. In particular, we discuss a formalism for approaching the lumped nonlinearity inherent in such a model using a circuit model and the application of wave digital filters (WDFs), which are of interest in that they allow simple stability verification, a property which is not generally guaranteed if one employs straightforward numerical methods. We present first a standard reed model, then its circuit representation, then finally the associated wave digital network. We then enter into some implementation issues, such as the solution of nonlinear algebraic equations, and the removal of delay-free loops, and present simulation results.