## Frequency Response Data (FRD) Models

### Frequency Response Data

In the Control System Toolbox™ software, you can use `frd`

models to store, manipulate,
and analyze frequency response data. An `frd`

model stores a
vector of frequency points with the corresponding complex frequency response data
you obtain either through simulations or experimentally.

For example, suppose you measure frequency response data for the SISO system you
want to model. You can measure such data by driving the system with a sine wave at a
set of frequencies *ω*_{1}, *ω*_{2}, ,...,*ω*_{n}, as shown:

At steady state, the measured response
*y _{i}*(

*t*) to the driving signal at each frequency

*ω*

_{i}takes the following form:

$${y}_{i}\left(t\right)=a\mathrm{sin}\left({\omega}_{i}t+b\right),\text{\hspace{1em}}i=1,\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}n.$$

The measurement yields the complex frequency response *G* at each
input frequency:

$$G\left(j{\omega}_{i}\right)=a{e}^{jb},\text{\hspace{1em}}i=1,\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}n.$$

You can do most frequency-domain analysis tasks on `frd`

models, but you cannot perform time-domain simulations with them. For information on
frequency response analysis of linear systems, see Chapter 8 of [1].

### Commands for Creating FRD Models

Use the following commands to create FRD models.

Command |
Description |
---|---|

`frd` | Create `frd` objects from frequency response
data. |

`frestimate` (Simulink Control Design) | Create `frd` objects by estimating the
frequency response of a Simulink^{®} model. This approach requires Simulink
Control Design™ software. See Offline Frequency Response Estimation (Simulink Control Design) for more
information. |

### Create Frequency-Response Model from Data

This example shows how to create a single-input, single-output (SISO)
frequency-response model using `frd`

.

A frequency-response model stores a vector of frequency points with corresponding complex frequency response data you obtain either through simulations or experimentally. Thus, if you measure the frequency response of your system at a set of test frequencies, you can use the data to create a frequency response model:

Load the frequency response data in

`AnalyzerData.mat`

.load AnalyzerData

This command loads the data into the MATLAB

^{®}workspace as the column vectors`freq`

and`resp`

. The variables`freq`

and`resp`

contain 256 test frequencies and the corresponding complex-valued frequency response points, respectively.**Tip**To inspect these variables, enter:

whos freq resp

Create a frequency response model.

sys = frd(resp,freq);

`sys`

is an `frd`

model object, which is a data
container for representing frequency response data.

You can use `frd`

models with many frequency-domain analysis
commands. For example, visualize the frequency response data using `bode`

.

**Tip**

By default, the `frd`

command assumes that the frequencies
are in radians/second. To specify different frequency units, use the
`TimeUnit`

and `FrequencyUnit`

properties
of the `frd`

model object. For example:

sys = frd(resp,freq,'TimeUnit','min','FrequencyUnit','rad/TimeUnit')

sets the frequency units to radians/minute.

## See Also

`frd`

| `frestimate`

(Simulink Control Design)