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Dr. Raviv Raich
Midterm I (Feb. 11, 2008)
The duration of the exam is ±fty minutes (3:00pm3:50pm). Only one sheet
of formulae is allowed. No calculators are allowed. Return this copy of the
exam form along with formulae sheet and your notes.
1. (50%) Let
p
(
t
) be the periodic signal with period
T
de±ned in [

T/
2
, T/
2]
by:
p
(
t
) =
1
τ

t

<
τ
2
0

t
 ≥
τ
2
···
···

T
T

τ
2
0
τ
2
1
τ
t
p
(
t
)
(a) (15%) Find and sketch
P
(
jω
), the continuoustime Fourier transform
(FT) of
p
(
t
).
(b) (10%) Consider the following two special cases: (i)
τ
→
0 (ii)
τ
=
T
.
For each case, write
p
(
t
) and
P
(
jω
) in a simpli±ed form and provide
a sketch for each.
(c) (25%) The signal
p
(
t
) goes through an LTI system with an impulse
response
h
(
t
) whose FT
H
(
jω
) is given by
H
(
jω
)
1

3
π
T
3
π
T
ω
The resulting signal is given by
y
(
t
) =
p
(
t
)
*
h
(
t
). Find
y
(
t
) in closedform.
(Hint: your answer should not include complexvalued numbers).
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 Winter '09
 RAICH

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