ECE634 Signals and Systems II, Spring 2009 - Lecture 17, March 2
Daniel S. Brogan
1
4.8 Frequency Response of an LTIC System
•
This section assumes that
0
s
j
j
j
σ
ω
ω
ω
=
+
=
+
=
, i.e. we are only concerned with the
steady-state component of the response.
Since the frequency response of an LTIC system
can be defined as
( )
(
)
(
)
(
)
j
H
j
H
s
H
j
H
j
e
ω
ω
ω
∠
=
=
the response to an input at some frequency
ω
defined as
( )
(
)
cos
x t
A
t
ω
θ
=
+
will produce
the output
( )
( )
(
)
(
)
(
)
(
)
cos
y t
x t H
j
A H
j
t
H
j
ω
ω
ω
θ
ω
=
=
+
+ ∠
Note that the magnitude and phase of the output may vary with frequency.
•
Example 4.23 (Lathi p.424)
Find the frequency response (amplitude and phase response) of a system whose transfer
function is
( )
0.1
5
s
H
s
s
+
=
+
Also, find the system response
( )
y t
if the input
( )
x t
is
(a)
(
)
cos 2
t
(b)
(
)
cos 10
50
t
−
°
(
)
0.1
5
j
H
j
j
ω
ω
ω
+
=
+
(
)
2
2
2
2
2
2
0.1
0.01
5
25
H
j
ω
ω
ω
ω
ω
+
+
=
=
+
+
(
)
1
1
tan
tan
0.1
5
H
j
ω
ω
ω
−
−
⎛
⎞
⎛
⎞
∠
=
−
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠

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