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What is a Model?

For our purposes, a model is any form of computation that predicts the state $ \underline{x}(t)$ at some future time $ t$ of a physical object or phenomenon based on

  1. the object's initial state $ \underline{x}(0)$
  2. any ``input'' (external) forces $ \underline{f}(t)$ on the object

\epsfig{file=eps/model.eps,width=4in}

In our case, typically,

\begin{eqnarray*}
\underline{f}(t) &=& \mbox{vector of \emph{performance control} variables}\\
\mbox{Object} &=& \mbox{\emph{musical instrument} and/or \emph{audio effects}}\\
\underline{x}(t) &=& \mbox{\emph{object state}}
\end{eqnarray*}

Output sound determined by object state



Subsections
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Download IntroPM.pdf
Download IntroPM_2up.pdf
Download IntroPM_4up.pdf

``Introduction to Physical Signal Models'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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