Higher Order Models

The preceding sections were concerned with modeling first-order continuous-time systems (the ideal mass in particular) using first-order discrete-time models. Advantages of this approach include (1) minimized computational expense, (2) an alias-free mapping of the plane to the plane, and (3) the possibility of preserving a physical intepretation of the state variables (which can lead to superior numerical performance). However, to achieve a better match to certain characteristics, such as the system frequency response, one may use arbitrarily high model orders. Such a ``filter design'' approach is discussed in §R.3 below.

---

Order a Hardcopy of Physical Audio Signal Processing

Previous: Practical Considerations
Next: ``Traveling Waves'' in Lumped Systems

---

written by 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.