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<math> A = T\widehat{A}T^*, \quad B = T\widehat{B}, \quad C = \widehat{C}T^*, \quad D = 0,</math> |
<math> A = T\widehat{A}T^*, \quad B = T\widehat{B}, \quad C = \widehat{C}T^*, \quad D = 0,</math> |
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+ | with |
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− | with the matrix <math> T </math> defined using <math> 2\times 2 </math> diagonal blocks. |
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+ | <math> T = \left[\begin{array}{ccc} T_0 & & \\ & \ddots & \\ & & T_0 \end{array}\right] </math>, |
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− | |||
+ | for <math>T_0 = \frac{1}{\sqrt{2}}\left[\begin{array}{cc} 1 & -j\\ 1 & j \end{array}\right]</math>. |
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== Example == |
== Example == |
Revision as of 13:18, 28 November 2011
Introduction
On this page you will find a purely synthetic parametric model. The goal is to have a simple parametric model which one can use to experiment with different system orders, parameter values etc.
System description
The parameter scales the real part of the system poles, that is,
.
If the system is in pole-residue form, then
which has the state-space realisation
Notice that the system matrices have complex entries.
For simplicity, assume that is even,
, and that all system poles are complex and ordered in complex conjugate pairs, i.e.
Which also implies that the residues form complex conjugate pairs
Then a realization with matrices having real entries is given by
with
,
for
.