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EE 448 Final Exam
May 3, 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) (5 points) Consider an analog signal
g
a
(
t
)
with highest frequency
Ω
m
. Let
g
[
n
]=
g
a
(
t
)

t
=
nT
Write down a frequencydomain expression that relates the DTFT
G
(
e
jω
)
of
g
[
n
]
to the CTFT
G
a
(
j
Ω)
of
g
a
(
t
)
.
How should you choose
T
to avoid aliasing?
(b) (5 points) Write down the bilinear transform and an expression that relates analog frequency
Ω
to digital fre
quency
ω
.
(c) (3 points each) Determine whether the following statements are true or false. Brieﬂy justify your answer.
i. An LTI system is BIBO stable if and only if its ROC is outside the unit circle.
ii. If
f
(
n
)
is an eigenfunction to an LTI system, the output of the system subject to the input
f
(
n
)
can be
expressed as
cf
(
n
)
, where
c
is a constant.
iii. It is possible to design zerophase causal digital ﬁlters.
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