General Modeling Procedure

While each situation tends to have special opportunities, the following procedure generally works well:

1. Formulate a state-space model.
2. If it is nonlinear, use numerical time-integration:
   • Explicit (causal finite difference scheme)
   • Implicit (iteratively solved each time step)
   • Semi-Implicit (truncated iterations of Implicit)
   There are many other descriptions of nonlinear systems to consider, some of which will be noted as we proceed.
3. In the linear case, diagonalize the state-space model to obtain the modal representation.
   • Implement isolated modes as second-order filters (``biquads'').
   • Implement quasi-harmonic mode series as digital waveguides.