Estimate impulse response using prewhitened-based correlation analysis
[ir,R,cl] = cra(data,M,na,plot)
cra prewhitens the input sequence; that is,
a filter chosen so that the result is as uncorrelated (white) as possible.
y is subjected to the same filter, and
then the covariance functions of the filtered
computed and graphed. The cross correlation function between (prewhitened)
input and output is also computed and graphed. Positive values of
the lag variable then correspond to an influence from
later values of
y. In other words, significant
correlation for negative lags is an indication of feedback from
A properly scaled version of this correlation function is also
an estimate of the system's impulse response
This is also graphed along with 99% confidence levels. The output
ir is this impulse response estimate,
so that its first entry corresponds to lag zero. (Negative lags are
ir.) In the plot, the impulse response
is scaled so that it corresponds to an impulse of height 1
duration T, where T is the
sample time of the data.
Number of lags for which the covariance/correlation functions are computed.
Order of the AR model to which the input is fitted.
For the prewhitening, the input is fitted to an AR model of
Plot display control.
Specify plot as one of the following integers:
Estimated impulse response.
The first entry of
99 % significance level for the impulse response.
Compare a second-order ARX model's impulse response with the one obtained by correlation analysis.
load iddata1 z = z1; ir = cra(z); m = arx(z,[2 2 1]); imp = [1;zeros(20,1)]; irth = sim(m,imp); subplot(211) plot([ir irth]) title('Impulse Responses') subplot(212) plot([cumsum(ir),cumsum(irth)]) title('Step Responses')
An often better alternative to
impulseest, which use a high-order FIR
model to estimate the impulse response.