Extracting Parametric Resonators from a Nonparametric Impulse Response

As mentioned in §8.7.1 above, 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.

Commuted synthesis is a technique in which the body resonator is commuted with the string model, as shown in Fig.8.10, in order to avoid having to implement a large body filter at all [443,233,230].^9.18In 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.