), comprised of three components,
x
(
t
) = 1 + 2 cos(
πt
) + 0
.
5 cos(10
πt
)
is illustrated here:
0
2
4
6
8
10
4
2
0
2
4
x(t) [INPUT SIGNAL]
t [SEC.]
This signal,
x
(
t
), is filtered with each of six different continuoustime LTI filters. The frequency response of each
of the six systems are shown below. (For

ω

>
3
π
, each frequency response has the value it has at

ω

= 3
π
.)
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 1
ω
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 2
ω
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 3
ω
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 4
ω
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 5
ω
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 6
ω
The six output signals are shown below, but they are not numbered in the same order.
114
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 1
t [SEC.]
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 2
t [SEC.]
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 3
t [SEC.]
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 4
t [SEC.]
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 5
t [SEC.]
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 6
t [SEC.]
Match each output signal to the system that was used to produce it by completing the table.
System
Output signal
1
2
3
4
5
6
115
2.7.30 A signal
x
(
t
), comprised of three components,
x
(
t
) = 1 + 0
.
5 cos(
πt
) + 2 cos(6
πt
)
is illustrated here:
0
2
4
6
8
10
4
2
0
2
4
x(t) [INPUT SIGNAL]
t [SEC.]
This signal,
x
(
t
), is filtered with each of six different continuoustime LTI filters. The frequency response of each
of the six systems are shown below. (For

ω

>
3
π
, each frequency response has the value it has at

ω

= 3
π
.)
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 1
ω
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 2
ω
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 3
ω
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 4
ω
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 5
ω
3π
2π
π
0
π
2π
3π
0
0.5
1
FREQUENCY RESPONSE 6
ω
The six output signals are shown below, but they are not numbered in the same order.
116
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 1
t [SEC.]
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 2
t [SEC.]
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 3
t [SEC.]
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 4
t [SEC.]
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 5
t [SEC.]
0
2
4
6
8
10
4
2
0
2
4
OUTPUT SIGNAL 6
t [SEC.]
Match each output signal to the system that was used to produce it by completing the table.
System
Output signal
1
2
3
4
5
6
117
2.7.31 Each of the two continuoustime signals below are processed with each of four LTI systems.
The two input
signals, illustrated below, are given by:
Input signal 1:
0
.
6 cos(3
πt
) + 2 cos(17
πt
)
Input signal 2:
2 cos(3
πt
) + 0
.
6 cos(17
πt
)
The frequency responses
H
f
(
ω
) are shown below.
Indicate how each of the output signals are produced by
completing the table below (copy the table onto your answer sheet). Note: one of the output signals illustrated
below will appear twice in the table (there are seven distinct output signals).
Input signal
System
Output signal
1
1
1
2
1
3
1
4
2
1
2
2
2
3
2
4
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
3
2
1
0
1
2
3
INPUT SIGNAL 1
TIME (SECONDS)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
3
2
1
0
1
2
3
INPUT SIGNAL 2
TIME (SECONDS)
118
ω

20
π

10
π
0
10
π
20
π
H
f
1
(
ω
)
1
ω

20
π

10
π
0
10
π
20
π
H
f
2
(
ω
)
1
1
ω

20
π

10
π
0
10
π
20
π
H
f
3
(
ω
)
1
ω

20
π

10
π
0
10
π
20
π
H
f
4
(
ω
)
1
1
119
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
3
2
1
0
You've reached the end of your free preview.
Want to read all 149 pages?
 Spring '08
 staff
 Digital Signal Processing, Signal Processing, LTI system theory, Impulse response, Inverse Systems