Specifications

freqresp
16-85
16freqresp
Purpose Compute frequency response over grid of frequencies
Syntax H = freqresp(sys,w)
Description H = freqresp(sys,w) computes the frequency response of the LTI model sys
at the real frequency points specified by the vector w. The frequencies must be
in radians/sec. For single LTI Models,
freqresp(sys,w) returns a 3-D array H
with the frequency as the last dimension (see “Arguments” below). For LTI
arrays of size
[Ny Nu S1 ... Sn], freqresp(sys,w) returns a
[
Ny-by-Nu-by-S1-by-...-by-Sn]length(w)array.
Incontinuoustime, theresponseat a frequency
ω
isthe transferfunctionvalue
at . For state-space models, this value is given by
In discrete time,the real frequencies
w(1),..., w(N) are mapped to points on the
unit circle using the transformation
where is the sample time. The transfer function is then evaluated at the
resulting values. The default is used for models with unspecified
sample time.
Remark If sys is an FRD model, freqresp(sys,w), w can only include frequencies in
sys.frequency. Interpolation and extrapolation are not supported. To
interpolate an FRD model, use
interp.
Arguments The output argument H is a 3-D array with dimensions
For SISO systems,
H(1,1,k) gives the scalar response at the frequency w(k).
For MIMO systems, the frequency response at
w(k) is H(:,:,k),amatrixwith
as many rows as outputs and as many columns as inputs.
Example Compute the frequency response of
sj
ω
=
Hj
ω()
DCj
ω
IA–
()
1–
B+=
ze
j
ω
T
s
=
T
s
zT
s
1=
number of outputs
()
number of inputs
()×
length of
w()×