EE 448 Midterm Exam
March 8, 2004
Name:
ID (last 4 digits):
Score:
Instructions:
This exam is closedbook and closednotes with the exception of an
8
.
5
×
11
crib sheet. You have 2 hours
to complete the exam. Write your name and ID number on all pages of your answers.
Show all work for full credit. Mark
your final answers.
Good luck!
1. (40 points) Mixed Problems:
(a) (4 points) Write down the expression of the
N
point DFT
X
[
k
]
of a sequence
x
[
n
]
, and the expression of the
corresponding IDFT.
(b) (4 points) Write down the expression of the
z
transform
X
(
z
)
of sequence
x
[
n
]
. What does ROC stand for?
(c) (6 points; 2 points each) Consider an
N
point sequence
x
1
[
n
]
,
0
≤
n
≤
N
−
1
, and an
M
point sequence
x
2
[
n
]
,
0
≤
n
≤
M
−
1
:
i. Let
y
L
[
n
]
denote the linear convolution of
x
1
[
n
]
and
x
2
[
n
]
. Write down an analytical expression that relates
y
L
[
n
]
to
x
1
[
n
]
and
x
2
[
n
]
. What is the length of
y
L
[
n
]
?
ii. Let
y
C
[
n
]
denote an
L
point circular convolution of
x
1
[
n
]
and
x
2
[
n
]
. Write down an analytical expression
that relates
y
C
[
n
]
to
x
1
[
n
]
and
x
2
[
n
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 Spring '08
 
 Digital Signal Processing, LTI system theory, 2 hours, Impulse response, 4 digits

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