Plot the Noise Spectrum at the Command Line

To plot the disturbance spectrum of an input-output model or the output spectrum of a time series model, use spectrum. To customize such plots, or to turn on the confidence region view programmatically for such plots, use spectrumplot instead.

To determine if your estimated noise model is good enough, you can compare the output spectrum of the estimated noise-model H to the estimated output spectrum of v(t). To compute v(t), which represents the actual noise term in the system, use the following commands:

ysimulated = sim(m,data);
v = ymeasured-ysimulated;

ymeasured is data.y. v is the noise term v(t), as described in What Does a Noise Spectrum Plot Show? and corresponds to the difference between the simulated response ysimulated and the actual response ymeasured.

To compute the frequency-response model of the actual noise, use spa:

V = spa(v);

The toolbox uses the following equation to compute the noise spectrum of the actual noise:

${\Phi }_{v}\left(\omega \right)=\sum _{\tau =-\infty }^{\infty }{R}_{v}\left(\tau \right){e}^{-i\omega \tau }$

The covariance function ${R}_{v}$ is given in terms of E, which denotes the mathematical expectation, as follows:

${R}_{v}\left(\tau \right)=Ev\left(t\right)v\left(t-\tau \right)$

To compare the parametric noise-model H to the (nonparametric) frequency-response estimate of the actual noise v(t), use spectrum:

spectrum(V,m)

If the parametric and the nonparametric estimates of the noise spectra are different, then you might need a higher-order noise model.