User`s guide

Identifying Impulse-Response Models
q is the shift operator,defined by t he followin g equation:
Gq gkq q ut ut
k
k
() () () ( )==−
−
=
∞
−
∑
1
1
1
For impulse response, the algorithm estimates impulse response coef ficients
g for both the single- and multiple-output data. The i mpulse response is
estimated as a high-order, noncausal FIR model:
yt g mut m g ut g ut
gut
() ( ) ( ) ( ) ( ) ( ) ()
() (
=− + ++− ++
+−
… 110
1 11) ( ) ( )++ −… gnut n
The estimation algorithm prefilters the data such that the input is as white
as possible. It then computes the correlations from the prefiltered data to
obtain the FIR coeffi cients.
g is also estimated for negative lags, which takes into account any noncausal
effects from input to output. Noncausal effects can result from feedback. The
coefficients are computed using the least-squares method.
For a multiple-input or multiple-output system, the impulse response g
k
is an
ny-by-nu matrix, w here ny is the number of outputs and nu is the number
of inputs. The i-jth element of the impulse response matrix describes the
behavior of the ith output after a n impulse in the jth input.
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