User`s guide

freqresp
11-84
11freqresp
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.
Incontinuous time,the responseat a frequencyω isthe transferfunction value
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 t hen 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 o nly include frequencies in
sys.frequency.
Arguments The output argument H is a 3-D array with dimensions
For SISO systems,
H(1,1,k) gives the scalar response at t he frequency w(k).
For MIMO systems, the frequency responseat
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=
Hjω() DCjωIA–()
1
–
B+=
ze
j
ω
T
s
=
T
s
z
T
s
1
=
number of outputs
()
number of inputs
()×
length of
w()×