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.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.