## 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.