Body-Model Factoring

In commuted synthesis, it is often helpful to factor out the least-damped resonances in the body model for implementation in parametric form (e.g., as second-order filters, or ``biquads''). The advantages of this are manifold, including the following:

• The excitation table is shortened (now containing only the most damped modal components).
  
• The excitation table signal-to-quantization-noise ratio is improved.
  
• The most important resonances remain parametric, facilitating real-time control. In other words, the parametric resonances can be independently modulated to produce interesting effects.
  
• Multiple body outputs become available from the parametric filters.
  
• Resonators may be already available in a separate effects unit, making them ``free.''
  
• A memory vs. computation trade-off is available for cost optimization.

Techniques for carrying out this factorization in practice are discussed in §8.8 [229].

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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.