Markov Parameters
The impulse response of a state-space model is easily found by direct
calculation using Eq.(G.1):
![\begin{eqnarray*}
\mathbf{h}(0) &=& C {\underline{x}}(0) + D\,\underline{\delta}...
... B\\ [5pt]
&\vdots&\\
\mathbf{h}(n) &=& C A^{n-1} B, \quad n>0
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/filters/img2054.png)
Note that we have assumed
(zero initial state or
zero initial conditions). The notation
denotes a
matrix having
along the diagonal and zeros
elsewhere.G.2
The impulse response of the state-space model can be summarized as
![]() |
(G.2) |
The impulse response terms for
are known as the
Markov parameters of the state-space model.
Note that each sample of the impulse response
is a
matrix.G.3 Therefore, it is not
a possible output signal, except when
. A better name might be
``impulse-matrix response''. In
§G.4 below, we'll see that
is the inverse z transform of the
matrix transfer-function of the system.
Given an arbitrary input signal
(and zero intial conditions
), the output signal is given by the convolution of the
input signal with the impulse response:
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Response from Initial Conditions
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Time Domain Filter Estimation