Digital Signal Processing I
Exam 3
Fall 2010
Session 41
3 Dec. 2010
Cover Sheet
Test Duration: 60 minutes.
Open Book but Closed Notes.
Calculators NOT allowed.
This test contains
two
problems.
All work should be done on blank 8.5” x 11” white sheets of paper.
Do
not
return this test sheet, just return your answer sheets.
1
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View Full DocumentDigital Signal Processing I
Exam 3
Fall 2010
Problem 1.
[65 pts]
For all parts of this problem, the reconstructed spectrum is computed according to Equa
tion 1 below:
Y
r
(
ω
) =
N

1
X
k
=0
Y
N
(
k
)
sin
h
N
2
±
ω

2
πk
N
²i
N
sin
h
1
2
±
ω

2
πk
N
²i
e

j
N

1
2
(
ω

2
πk
N
)
(1)
(a) Let
x
[
n
] be a discretetime rectangular pulse of length
L
= 5 and
h
[
n
] be a discretetime
rectangular pulse of length
M
= 3 as deﬁned below:
x
[
n
] =
u
[
n
]

u
[
n

5]
h
[
n
] =
u
[
n
]

u
[
n

3]
(i) With
X
N
(
k
) computed as the 12pt DFT of
x
[
n
] and
H
N
(
k
) computed as the
12pt DFT of
h
[
n
], the product
Y
N
(
k
) =
X
N
(
k
)
H
N
(
k
) is used in Eqn (1) with
N
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 Fall '08
 ZOLTOLSKI
 Digital Signal Processing, Signal Processing, Trigraph, 5pt, reconstructed spectrum Yr

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