General Modeling Procedure
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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A Simplified Starting Theory
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Digital Waveguide Modeling Elements