# spectrum

Plot or return output power spectrum of time series model or disturbance spectrum of linear input-output model

## Syntax

## Description

### Plot Results

`spectrum(`

plots the output power
spectrum of an identified time series model `sys`

)`sys`

or the
disturbance spectrum of an identified input-output model
`sys`

. The function chooses the frequency range and
number of points automatically.

If

`sys`

is a time series model, then`sys`

represents the system:$$y(t)=He(t)$$

Here,

*e*(*t*) is a Gaussian white noise and*y*(*t*) is the observed output.`spectrum`

plots |*H*'*H*|, scaled by the variance of*e*(*t*) and the sample time.If

`sys`

is an input-output model,`sys`

represents the system:$$y(t)=Gu(t)+He(t)$$

Here,

*u*(*t*) is the measured input,*e*(*t*) is Gaussian white noise and*y*(*t*) is the observed output.In this case,

`spectrum`

plots the spectrum of the disturbance component*He*(*t*).

For discrete-time models with sample time
*T _{s}*,

`spectrum`

uses the transformation $$z={e}^{j\omega {T}_{s}}$$ to map the unit circle to the real frequency axis. The
function plots the spectrum only for frequencies smaller than the Nyquist
frequency π/*T*, and uses the default value of 1 time unit when Ts is unspecified.

_{s}`spectrum(sys1,...,sysN,`

creates a
spectrum plot of several identified models on a single plot. The
`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')`

uses red for
`sys1`

, yellow dash markers for `sys2`

,
and green `x`

markers for `sys3`

.

### Return Results

## Examples

## Input Arguments

## Output Arguments

**Introduced in R2012a**