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Department of Electrical and Computer Engineering
University of Maryland
College Park, Maryland
ENEE 322
A. Tits
Signal and System Theory
November 18, 2003
Second MidTerm Examination
Please make sure you answer all the questions.
Question 1 (4 pts):
Consider a continuoustime stable LTI system
S
with frequency response given by
H
F
(
ω
) =
n
1 if

ω

<
5
0 otherwise
.
When the input to this system is a periodic signal
x
with fundamental period
T
=
π
and Fourier series
coe±cients
a
k
it is found that the output
y
is identical to
x
. For what values of
k
is it guaranteed that
a
k
= 0? Explain.
Question 2 (11 pts):
Consider a continuoustime LTI system whose input
x
and output
y
are related via
the di²erential equation
2¨
y
(
t
) + 5 ˙
y
(
t
) + 2
y
(
t
) =
a
˙
x
(
t
) +
bx
(
t
)
,
where
a
and
b
are to be determined (see below).
(a) (2 pt) How many di²erent LTI systems satisfy this input/output relationship (for given
a
and
b
)?
Explain. One of these systems is stable. Is it causal? Explain.
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 Fall '03
 Tretter

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