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Relation of FDNs to State-Space Models

When the delay lines are only 1 sample long, a standard state-space model results:

\begin{eqnarray*}
\mathbf{x}(n+1) &=& \mathbf{A}\mathbf{x}(n) + \mathbf{u}(n)\\
\mathbf{y}(n) &=& \mathbf{x}(n)\nonumber
\protect
\end{eqnarray*}

When the delay-lines are not unit length, the state-space description of an FDN expands in a simple way.

Matlab includes many tools for state-space analysis and simulation, especially in the Control Systems Tool Box.


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``Computational Acoustic Modeling with Digital Delay'', by Julius O. Smith III and Nelson Lee,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-06-05 under the Creative Commons License (Attribution 2.5), by Julius O. Smith III and Nelson Lee
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA