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ENEE 241 02*
HOMEWORK ASSIGNMENT 3
Due Tue 02/17
Problem 3A
Consider the discretetime sinusoids
x
[
n
] = cos
±
7
πn
12

0
.
5
¶
and
y
[
n
] = cos(1
.
83
n

0
.
5)
(i) (3 pts.)
Which of the two sinusoids is periodic, and what is its fundamental period?
(ii) (3 pts.)
Use MATLAB to generate separate plots of
x
[
n
] and
y
[
n
] for
n
= 0
,...,
47.
(iii) (4 pts.)
Let
N
be the value of the period found in part (i). For what values of
ω
in [0
,π
] is
cos(
ωn
)
periodic with fundamental period
N
?
(iv) (3 pts.)
An equivalent form for
x
[
·
] is
x
[
n
] = cos(
ωn
+
φ
)
where
ω
is between
π
and 2
π
. What are the values of
ω
and
φ
?
(v) (2 pts.)
The sequence
v
[
·
] is formed by taking every fourth sample in
x
[
·
], i.e.,
v
[
n
] =
x
[4
n
]
Write an equation for
v
[
n
]. What is the period of
v
[
·
]?
(vi) (5 pts.)
Using phasors, express
y
[
n
]

y
[
n

1]

2
y
[
n

2]
as a single realvalued sinusoid.
Problem 3B
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
3
2
1
0
1
2
3
Two periods of the sinusoid
x
(
t
) =
A
cos(Ω
t
+
φ
) are plotted above. The value of
x
(0) equals

3sin(
π/
5).
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View Full Document (i) (6 pts.)
Determine
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This note was uploaded on 10/18/2011 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff

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