# modalfrf

Frequency-response functions for modal analysis

## Syntax

## Description

estimates a matrix of frequency response functions, `frf`

= modalfrf(`x`

,`y`

,`fs`

,`window`

)`frf`

,
from the excitation signals, `x`

, and the response signals,
`y`

, all sampled at a rate `fs`

. The
output, `frf`

, is an *H*_{1} estimate computed using Welch’s method with
`window`

to window the signals. `x`

and `y`

must have the same number of rows. If
`x`

or `y`

is a matrix, each column
represents a signal.

The system response, `y`

, is assumed to contain
acceleration measurements. To compute a frequency-response function starting
from displacement or velocity measurements, use the `'Sensor'`

argument.
`modalfrf`

always outputs the frequency-response
function in dynamic flexibility (receptance) format irrespective of the sensor
type.

specifies options using name-value arguments, using any combination of inputs
from previous syntaxes. Options include the estimator, the measurement
configuration, and the type of sensor measuring the system response.`frf`

= modalfrf(___,`Name,Value`

)

`[`

computes the frequency-response function of the identified model
`frf`

,`f`

] = modalfrf(`sys`

)`sys`

. Use estimation commands like `ssest`

(System Identification Toolbox), `n4sid`

(System Identification Toolbox), or `tfest`

(System Identification Toolbox) to create
`sys`

from time-domain input and output signals. This
syntax allows use only of the `'Sensor'`

name-value argument.
You must have a System Identification Toolbox™ license to use this syntax.

`modalfrf(___)`

with no output
arguments plots the frequency response functions in the current figure.
The plots are limited to the first four excitations and four responses.

## Examples

## Input Arguments

## Output Arguments

## References

[1] "Dynamic Stiffness, Compliance, Mobility, and more..." Siemens, last modified 2019, https://community.sw.siemens.com/s/article/dynamic-stiffness-compliance-mobility-and-more.

[2] Brandt, Anders. *Noise and Vibration Analysis: Signal Analysis and
Experimental Procedures*. Chichester, UK: John Wiley & Sons,
2011.

[3] Irvine, Tom. "An Introduction to Frequency Response Functions," Vibrationdata, 2000, https://vibrationdata.com/tutorials2/frf.pdf.

[4] Vold, Håvard, John Crowley, and G. Thomas Rocklin. "New Ways of Estimating Frequency
Response Functions." *Sound and Vibration*. Vol. 18, November 1984,
pp. 34–38.

## Version History

**Introduced in R2017a**

## See Also

`modalfit`

| `modalsd`

| `n4sid`

(System Identification Toolbox) | `tfestimate`

### Topics

- Modal Analysis of Identified Models
- System Identification Overview (System Identification Toolbox)
- System Identification Workflow (System Identification Toolbox)
- Supported Continuous- and Discrete-Time Models (System Identification Toolbox)