# freqresp

Evaluate system response over a grid of frequencies

## Syntax

## Description

Use `freqresp`

to evaluate the system response over a grid of
frequencies. To obtain the magnitude and phase data as well as plots of the frequency
response, use `bode`

instead.

`[`

returns the frequency response of the dynamic system model `H`

,`wout`

]
= freqresp(`sys`

)`sys`

at
frequencies `wout`

. `freqresp`

automatically determines
the frequencies based on the dynamics of `sys`

. For more information
about frequency response, see Frequency Response.

## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

For transfer functions or zero-pole-gain models, `freqresp`

evaluates the
numerator(s) and denominator(s) at the specified frequency points. For continuous-time
state-space models (*A*, *B*, *C*,
*D*), the frequency response is

$$\begin{array}{cc}D+C{(j\omega -A)}^{-1}B,& \omega =\end{array}{\omega}_{1},\dots ,{\omega}_{N}$$

For efficiency, *A* is reduced to upper Hessenberg form and the linear
equation (*jω − A*)*X* = *B* is solved at
each frequency point, taking advantage of the Hessenberg structure. The reduction to
Hessenberg form provides a good compromise between efficiency and reliability. For more
details on this technique, see [1].

## References

[1] Laub, A.J., "Efficient
Multivariable Frequency Response Computations," *IEEE ^{®} Transactions on Automatic Control*, AC-26 (1981), pp.
407-408.

## Version History

**Introduced before R2006a**