## 5aMU12. Reducing computational complexity in struck string physical models.

### Session: Friday Morning, December 6

### Time: 11:20

**Author: Stefan Bilbao**

**Location: Ctr. for Comput. Res. in Music and Acoust., Stanford Univ., 660 Lomita Dr., Stanford, CA 94305-8180**

**Abstract:**

Chaigne and Askenfelt recently published a paper in which they described a
physical model of a struck string [J. Acoust. Soc. Am. 95, 1112--1118 (1994)].
The model is based on a finite difference approximation to a particular partial
differential equation, and involves updating transversal displacement at
discrete locations along a string. A nonlinear hammer is also incorporated into
the model. It is shown in this paper that, if it is desired to know the output
only at one particular point (or perhaps a weighted linear combination of
points) along the string, then the number of operations required in order to
compute the synthesized output can be reduced. This is done by expressing
Chaigne and Askenfelt's model in state space form, and by then performing
appropriate coordinate transformations to ``modal`` coordinates. What is more,
computational complexity in the modal coordinates will be independent of the
number of spatial derivatives modeled, so that accurate modeling of dispersion
can be achieved at no extra cost. The coordinate-changing method applies equally
well to the case of spatially varying media, and is simply extended to models
which are higher order in time.

ASA 132nd meeting - Hawaii, December 1996