Output power spectrum of time series models
spectrum(sys)
spectrum(sys,{wmin, wmax})
spectrum(sys,w)
spectrum(sys1,...,sysN,w)
ps = spectrum(sys,w)
[ps,w] = spectrum(sys)
[ps,w,sdps]
= spectrum(sys)
spectrum(
creates
an output power spectrum plot of the identified time series model sys
)sys
.
The frequency range and number of points are chosen automatically.
sys
is a time series model, which represents
the system:
$$y(t)=He(t)$$
Where, e(t)
is a Gaussian white noise and y(t)
is
the observed output.
spectrum
plots abs(H'H)
,
scaled by the variance of e(t)
and the sample time.
If sys
is an inputoutput model, it represents
the system:
$$y(t)=Gu(t)+He(t)$$
Where, u(t)
is the measured input, e(t)
is
a Gaussian white noise and y(t)
is the observed
output.
In this case, spectrum
plots the spectrum
of the disturbance component He(t)
.
spectrum(
creates
a spectrum plot for frequencies ranging from sys
,{wmin
, wmax
})wmin
to wmax
.
spectrum(
creates
a spectrum plot using the frequencies specified in the vector sys
,w
)w
.
spectrum(
creates
a spectrum plot of several identified models on a single plot. The sys1,...,sysN
,w
)w
argument
is optional.
You can specify a color, line style and marker for each model. For example:
spectrum(sys1,'r',sys2,'y',sys3,'gx');
returns
the power spectrum amplitude of ps
= spectrum(sys
,w
)sys
for the specified
frequencies, w
. No plot is drawn on the screen.
[
returns
the frequency vector, ps
,w
] = spectrum(sys
)w
, for which the output
power spectrum is plotted.
[
returns the estimated
standard deviations of the power spectrum.ps
,w
,sdps
]
= spectrum(sys
)
For discretetime models with sample time Ts
, spectrum
uses
the transformation z = exp(j*w*Ts)
to map the unit
circle to the real frequency axis. The spectrum is only plotted for
frequencies smaller than the Nyquist frequency pi/Ts
,
and the default value 1 (time unit) is assumed when Ts is unspecified.

Identified model. If $$y(t)=He(t)$$ Where, If $$y(t)=Gu(t)+He(t)$$ Where, 

Minimum frequency of the frequency range for which the output power spectrum is plotted. Specify 

Maximum frequency of the frequency range for which the output power spectrum is plotted. Specify 

Frequencies for which the output power spectrum is plotted. Specify 

Identified systems for which the output power spectrum is plotted. 

Power spectrum amplitude. If For amplitude values in dB, type 

Frequency vector for which the output power spectrum is plotted. 

Estimated standard deviation of the power spectrum. 