Extracting Parametric Resonators from a Nonparametric Impulse Response

Commuted synthesis is a technique in which the body resonator is commuted with the string model, as shown in Fig. 4.25, in order to avoid having to implement a large body filter at all [416,216,213].^Q.1In commuted synthesis, the excitation (e.g., plucking force versus time) can be convolved with the resonator impulse response to provide a single aggregate excitation signal. This signal is short enough to store in a look-up table, and a note is played by simply summing it into the string.

A valuable way of shortening the excitation table in commuted synthesis is to factor the body resonator into its most-damped and least-damped modes. The most-damped modes are then commuted and combined with the excitation in impulse-response form. The least-damped modes can be left in parametric form as recursive digital filter sections. Advantages of this factoring include the following:

• The excitation table is shortened.
  
• The excitation table signal-to-quantization-noise ratio is improved.
  
• The most important resonances remain parametric, facilitating real-time control.
  
• Multiple body outputs become available.
  
• Resonators may be already available in a separate effects unit, making them ``free.''
  
• A memory vs. computation trade-off is available for cost optimization.