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Transfer Function of a State Space Filter
The transfer function can be defined as the 
transform of
the impulse response:
![$\displaystyle H(z) \isdef \sum_{n=0}^{\infty} h(n) z^{-n}
= D + \sum_{n=1}^{\in...
...z^{-n}
= D + z^{-1}C \left[\sum_{n=0}^{\infty} \left(z^{-1}A\right)^n\right] B
$](http://www.dsprelated.com/josimages_new/filters/img2070.png)
Note that if there are
inputs and 
outputs, 
is a 
transfer-function matrix
(or ``matrix transfer function'').
Subsections
Previous: Complete Response
Next: Example State Space Filter Transfer Function
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Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.
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