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

- Formulate a
*state-space model*. - 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)

- 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*.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University