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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 $ s$ plane to the $ z$ 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 §P.3 below.


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[How to cite and copy this work] 
``Physical Audio Signal Processing for Virtual Musical Instruments and Digital Audio Effects'', by Julius O. Smith III, (December 2005 Edition).
Copyright © 2006-07-01 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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