freqresp
Frequency response over grid
Syntax
[H,wout]
= freqresp(sys)
H = freqresp(sys,w)
H = freqresp(sys,w,units)
[H,wout,covH]
= freqresp(idsys,...)
Description
[
returns the frequency response of
the dynamic system model H
,wout
]
= freqresp(sys
)sys
at
frequencies wout
. The freqresp
command
automatically determines the frequencies based on the dynamics of sys
.
returns the frequency
response on the real frequency grid specified by the vector H
= freqresp(sys
,w
)w
.
explicitly
specifies the frequency units of H
= freqresp(sys
,w
,units
)w
with units
.
[
also returns
the covariance H
,wout
,covH
]
= freqresp(idsys
,...)covH
of the frequency response
of the identified model idsys
.
Input Arguments

Any dynamic system model or model array. 

Vector of real frequencies at which to evaluate the frequency
response. Specify frequencies in units of 

Units of the frequencies in the input frequency vector
Default: 

Any identified model. 
Output Arguments

Array containing the frequency response values. If If If 

Vector of frequencies corresponding to the frequency response
values in 

Covariance of the response 
Examples
More About
Algorithms
For transfer functions or zeropolegain models, freqresp
evaluates
the numerator(s) and denominator(s) at the specified frequency points.
For continuoustime statespace 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. See [1] for more details on this technique.
Alternatives
Use evalfr
to evaluate
the frequency response at individual frequencies or small numbers
of frequencies. freqresp
is optimized for mediumtolarge
vectors of frequencies.
References
[1] Laub, A.J., "Efficient Multivariable Frequency Response Computations," IEEE^{®} Transactions on Automatic Control, AC26 (1981), pp. 407408.