ECE220
Signals and Information
Spring 2008
Homework 1: Due Monday, February 4, 10:00am
Drop your homework in the collection box marked
”ECE220 Spring 2008, homeworks”
which is
located at the south entrance to 219 Phillips,
Print your
name, NetId, and lab section
in the top right corner on all pages.
NOTE: This homework is based on lectures 15.
Problem 1
Find the cyclic frequency, radian frequency, amplitude, phase shift and time shift of the following
signals:
1.
x
(
t
) = 4
.
8 cos(876
πt
+
π
128
)
2.
x
(
t
) = 0
.
25 sin(20
πt
+
π
3
)
3.
x
(
t
) = (1

j)(1 + j)(1

2 cos
2
(4096
πt
)) where j =
√

1
Problem 2
Let
x
(
t
) = sin(4
πt
). Plot
1.
y
(
t
) =
x
(
t

1
8
)
2.
z
(
t
) = 2

x
(
t
+
1
16
)

Remember to label axis.
Problem 3
Express the following number in the form
Ae
j
θ
:
1.
e
j
2
5
π
+
e
j
4
5
π
2. (
√
15

j)
2
3.
I
m
(50 cos(2
π
100
t
) for
t
∈
[0
,
2
π
]
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/
(2

j)
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 Spring '05
 JOHNSON
 Frequency, Phase Shift, Sine wave, time shift

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