FDN and State Space Descriptions
When
in Eq.
(2.10), the FDN (Fig.2.28)
reduces to a normal state-space model (§1.3.7),
The matrix
![$ \mathbf{A}={\bm \Gamma}\mathbf{Q}$](http://www.dsprelated.com/josimages_new/pasp/img545.png)
![$ \mathbf{x}(n) = [x_1(n), x_2(n), x_3(n)]^T$](http://www.dsprelated.com/josimages_new/pasp/img546.png)
![$ n$](http://www.dsprelated.com/josimages_new/pasp/img146.png)
![$ \mathbf{x}(n)$](http://www.dsprelated.com/josimages_new/pasp/img547.png)
![\begin{eqnarray*}
\mathbf{u}_+(n) &\isdef & \mathbf{u}(n+1)\\
\mathbf{y}_+(n) &\isdef & \mathbf{y}(n+1)
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/pasp/img548.png)
to follow normal convention for state-space form.
Thus, an FDN can be viewed as a generalized state-space model for a
class of th-order linear systems--``generalized'' in the sense
that unit delays are replaced by arbitrary delays. This
correspondence is valuable for analysis because tools for state-space
analysis are well known and included in many software libraries such
as with matlab.
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Single-Input, Single-Output (SISO) FDN
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Time Varying Comb Filters