Signals and Systems Midterm
10:20a.m. ~ 12:20p.m., May 2, Fri., 2008
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Closed book, but open 1 sheet (both sides, 2 pages) of personal notes of A4 size
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Total score: 120
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Total 4 pages in one B4 sheet
1.
[10]
Consider a system
H
to be tested as being
memoryless
,
causal
,
linear
,
time invariant
,
and
invertible
. Three signals
1
( )
x t
,
2
( )
x
t
, and
3
( )
x
t
are sent to the system, and the
corresponding output signals
1
( )
y t
,
2
( )
y
t
, and
3
( )
y
t
are obtained as shown in Figure 1.
Based on the three input-output pairs, is it possible to determine each of the five properties for
system
H
? If yes, what is it? If no, why? Justify your answer.
Figure 1
2.
Consider a system as shown in Figure 2, where
( )
h t
is the impulse response of the LTI
sub-system in the block, and 2D is the operation of time delay for 2 units.
Figure 2
h
(
t
)
2D
+
x
(
t
)
y
(
t
)
1 2 3 4 5
1
2
0
x
(
t
)
1
2
3
4
5
1
2
0
h
(
t
)
H
H
H
1 2
3 4 5
1
2
3
0
4
x
1
(
t
)
1 2
3 4 5
1
2
3
0
4
x
2
(
t
)
1 2
3 4 5
1
2
3
0
4
x
3
(
t
)
1 2 3 4 5
1
2
3
0
4
y
1
(
t
)
1 2 3 4 5
1
2
3
0
4
y
2
(
t
)
1 2 3 4 5
1
2
3
0
4
y
3
(
t
)

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