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1
Department of Electrical and Computer Engineering
The Ohio State University
WINTER 2008
ECE 700 Digital Signal Processing
11:30 AM-1:18 PM
3/11/08
Final Examination
Directions
•
You are allowed to have two sheets of paper with anything you want on it. No other
books or notes are allowed in the examination.
•
The examination has 6 questions and 14 pages. Each question is worth 20 points.
Please make sure that you answer all questions.
•
Write clearly and show all work for full credit.
•
If you are making any assumptions in solving any of the problems, please state these
clearly at the beginning of your solution.
•
The ECE Honor System applies to this examination. At the end of the examination, if
the pledge below applies, please sign your name in the line below the pledge.
“No aid given, received or observed during the course of this examination.”
Signature
Your name:

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2
1.
(20 points)
a.
Show that the two systems shown below are equivalent.
b.
Consider the system shown below. Express
y
[
n
] in terms of
x
[
n
]. Simplify
your expression as much as possible.
c.
For the system above, express
Y
(
z
) in terms of
X
(
z
)?
a.
For the LHS system,
y
1
[
n
]=
s
1
[3
n
],
s
1
[
n
] =
x
[2
n
], so
y
1
[
n
] =
x
[6
n
]
For the RHS system,
y
2
[
n
]=
s
2
[2
n
],
s
2
[
n
] =
x
[3
n
], so
y
2
[
n
] =
x
[6
n
]
So LHS is same as RHS
b.
Using result of part a, exchange middle two blocks. Then
3 and
3 cancel leaving
2 and
2.
↑
↓
↓
↑
[ ], even
Output of
2 is [ ]
[2 ], and output of
2 is [ ]
2
0, otherwise
[ ], even
So [ ]
.
0, otherwise

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