ECE 220, Section 001
Final Exam Solutions
13 December 2005
Problem 1. (10 points)
Consider the pulse,
p
(
t
), in Equation 1:
p
(
t
)=
±
1
,
0
≤
t<
10
,
0
,
otherwise.
(1)
Express the signal
s
(
t
) in Equation 2 in terms of
p
(
t
).
s
(
t
0
,
t <
0
,

2
,
0
≤
5
,
1
,
5
≤
15
,
0
,t
≥
15.
(2)
Solution
The signal contains two pulses, one of width 50 = 5, and another of width 155
=10. The scaled signal
s
1
(
t
p
(2
t
±
1
,
0
≤
2
10
,
0
,
otherwise.
=
±
1
,
0
≤
5
,
0
,
otherwise,
has a width of Fve. The signal
s
2
(
t
p
(
t

5) =
±
1
,
0
≤
t

5
<
10
,
0
,
otherwise.
=
±
1
,
5
≤
15
,
0
,
otherwise,
has a width of 10. With these two signals we can write
s
(
t

2
s
1
(
t
)+
s
2
(
t
), so Fnally,
s
(
t

2
p
(2
t
p
(
t

5)
1