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Bode plot of frequency response, or magnitude and phase data

`bode(sys)`

`bode(sys1,sys2,...,sysN)`

`bode(sys1,LineSpec1,...,sysN,LineSpecN)`

`bode(___,w)`

```
[mag,phase,wout]
= bode(sys)
```

```
[mag,phase,wout]
= bode(sys,w)
```

```
[mag,phase,wout,sdmag,sdphase]
= bode(sys,w)
```

`bode(`

creates
a Bode plot of the frequency response of a dynamic
system model `sys`

)`sys`

. The plot displays
the magnitude (in dB) and phase (in degrees) of the system response
as a function of frequency. `bode`

automatically
determines frequencies to plot based on system dynamics.

If `sys`

is a multi-input, multi-output (MIMO)
model, then `bode`

produces an array of Bode plots,
each plot showing the frequency response of one I/O pair.

`bode(sys1,sys2,...,sysN)`

plots the frequency
response of multiple dynamic systems on the same plot. All systems
must have the same number of inputs and outputs.

`bode(sys1,`

specifies a
color, linestyle, and marker for each system in the plot.`LineSpec`

1,...,sysN,LineSpecN)

`bode(___,`

plots
system responses for frequencies specified by `w`

)`w`

.

If

`w`

is a cell array of the form`{wmin,wmax}`

, then`bode`

plots the response at frequencies ranging between`wmin`

and`wmax`

.If

`w`

is a vector of frequencies, then`bode`

plots the response at each specified frequency.

You can use `w`

with any of the input-argument
combinations in previous syntaxes.

When you need additional plot customization options, use

`bodeplot`

instead.

`bode`

computes the frequency response as
follows:

Compute the zero-pole-gain (

`zpk`

) representation of the dynamic system.Evaluate the gain and phase of the frequency response based on the zero, pole, and gain data for each input/output channel of the system.

For continuous-time systems,

`bode`

evaluates the frequency response on the imaginary axis*s*=*jω*and considers only positive frequencies.For discrete-time systems,

`bode`

evaluates the frequency response on the unit circle. To facilitate interpretation, the command parameterizes the upper half of the unit circle as:$$z={e}^{j\omega {T}_{s}},\text{\hspace{1em}}0\le \omega \le {\omega}_{N}=\frac{\pi}{{T}_{s}},$$

where

*T*is the sample time and_{s}*ω*is the Nyquist frequency. The equivalent continuous-time frequency_{N}*ω*is then used as the*x*-axis variable. Because $$H\left({e}^{j\omega {T}_{s}}\right)$$ is periodic with period 2*ω*,_{N}`bode`

plots the response only up to the Nyquist frequency*ω*. If_{N}`sys`

is a discrete-time model with unspecified sample time,`bode`

uses*T*= 1._{s}