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1
UCLA
Dept. of Electrical Engineering
EE114 Midterm exam
2/6/2008
This exam consists of five questions. Please show all steps leading to your
answers. An answer without explanation will not receive full credit.
GOOD LUCK!
1.
(20 points) DFT
Bold and underlined characters or numbers denote array elements at position zero (
n
=0).
Be sure to specify the position where
n
=0 in your results, when applicable.
(a)
Given the time signal
x
(
n
) = [
a
b c d], what is the 4point DFT (
X
(
k
)) as a function
of a, b, c, and d?
i.
Assuming
x
(
n
) is even
and periodic
with a period of 4 samples, the result
for
X
(
k
) is simplified. What is the simplified
X
(
k
) as a function of a, b, c,
and d?
ii.
Assuming
x
(
n
) is odd
and periodic
with a period of 4 samples, the result
for
X
(
k
) is simplified. What is the simplified
X
(
k
) as a function of a, b, c,
and d?
(b)
Assume that the 2point DFT of
x
(
n
)=[
a
b] is
X
(
k
)=[
A
B]. Calculate the 4point
DFT of
y
(
n
)=[
a
b a b],
Y
(
k
), as a function of A and B.
2.
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This note was uploaded on 11/12/2011 for the course EE 114 taught by Professor Vanschaar during the Spring '11 term at UCLA.
 Spring '11
 VanSchaar
 Electrical Engineering

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