frd (Function Reference)

Create a frequency response data (FRD) object or convert another model type to an FRD model

Syntax

sys = frd(response,frequency)
sys = frd(response,frequency,Ts)
sys = frd
sys = frd(response,frequency,ltisys)

sysfrd = frd(sys,frequency)
sysfrd = frd(sys,frequency,'Units',units)

Description

sys = frd(response,frequency) creates an FRD model sys from the frequency response data stored in the multidimensional array response. The vector frequency represents the underlying frequencies for the frequency response data. See Table 0-1, Data Format for the Argument response in FRD Models.

sys = frd(response,frequency,Ts) creates a discrete-time FRD model sys with scalar sample time Ts. Set Ts = -1 to create a discrete-time FRD model without specifying the sample time.

sys = frd creates an empty FRD model.

The input argument list for any of these syntaxes can be followed by property name/property value pairs of the form

```
'PropertyName',PropertyValue
```

You can use these extra arguments to set the various properties of FRD models (see the set command, or LTI Properties and Model-Specific Properties). These properties include 'Units'. The default units for FRD models are in 'rad/s'.

To force an FRD model sys to inherit all of its generic LTI properties from any existing LTI model refsys, use the syntax

```
sys = frd(response,frequency,ltisys)
```

sysfrd = frd(sys,frequency) converts a TF, SS, or ZPK model to an FRD model. The frequency response is computed at the frequencies provided by the vector frequency.

sysfrd = frd(sys,frequency,'Units',units)converts an FRD model from a TF, SS, or ZPK model while specifying the units for frequency to be units ('rad/s' or 'Hz').

Arguments

When you specify a SISO or MIMO FRD model, or an array of FRD models, the input argument frequency is always a vector of length Nf, where Nf is the number of frequency data points in the FRD. The specification of the input argument response is summarized in the following table.

Table 0-1: Data Format for the Argument response in FRD Models
Model Form

Response Data Format

SISO model

Vector of length Nf for which response(i) is the frequency response at the frequency frequency(i)

MIMO model with Ny outputs and Nu inputs

Ny-by-Nu-by-Nf multidimensional array for which response(i,j,k) specifies the frequency response from input j to output i at frequency frequency(k)

S1-by-...-by-Sn array of models with Ny outputs and Nu inputs

Multidimensional array of size [Ny Nu S1 ... Sn] for which response(i,j,k,:) specifies the array of frequency response data from input j to output i at frequency frequency(k)

**Table 0-1: Data Format for the Argument response in FRD Models**
Model Form		Response Data Format
SISO model		Vector of length `Nf` for which `response(i)` is the frequency response at the frequency `frequency(i)`
MIMO model with `Ny` outputs and `Nu` inputs		`Ny`-by-`Nu`-by-`Nf` multidimensional array for which `response(i,j,k)` specifies the frequency response from input `j` to output `i` at frequency `frequency(k)`
`S1`-by-`...`-by-`Sn` array of models with `Ny` outputs and `Nu` inputs		Multidimensional array of size [`Ny` `Nu` `S1` `...` `Sn]` for which `response(i,j,k,:)` specifies the array of frequency response data from input `j` to output `i` at frequency `frequency(k)`

Remarks

See Frequency Response Data (FRD) Models for more information on single FRD models, and Creating LTI Models for information on building arrays of FRD models.

Example

Type the commands

freq = logspace(1,2);
resp = .05*(freq).*exp(i*2*freq);
sys = frd(resp,freq)

to create a SISO FRD model.

See Also
chgunits Change units for an FRD model

frdata Quick access to data for an FRD model

set Set the properties for an LTI model

ss Create state-space models

tf Create transfer functions

zpk Create zero-pole-gain models

filt frdata