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100
6.003
(Spring
2010)
Final
Examination
May
20,
2010
Name:
Kerberos
Username:
Please
circle
your
section
number:
Section
Instructor
Time
1
Peter
Hagelstein
10
am
2
Peter
Hagelstein
11
am
3
Rahul
Sarpeshkar
1
pm
4
Rahul
Sarpeshkar
2
pm
Grades
will
be
determined
by
the
correctness
of
your
answers
(explanations
are
not
required).
Partial
credit
will
be
given
for
ANSWERS
that
demonstrate
some
but
not
all
of
the
important
conceptual
issues.
You
have
three
hours.
Please
put
your
initials
on
all
subsequent
sheets.
Enter
your
answers
in
the
boxes.
This
quiz
is
closed
book,
but
you
may
use
four
8
.
5
×
11 sheets
of
paper
(eight
sides
total).
No
calculators,
computers,
cell
phones,
music
players,
or
other
aids.
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x
[
n
]
α
0
α
1
α
2
α
3
α
4
0
3
6
9
12
−
3
−
6
2
Final
Examination
/
6.003:
Signals
and
Systems
(Spring
2010)
1.
Z
Transform
[10
points]
Find
the
Z
transform
of
x
[
n
] deﬁned
as
x
[
n
] =
α
å
n/
3
æ
u
[
n
]
where
α
represents
a
positive
real
number,
u
[
n
] represents
the
unitstep
function,
and
å
n/
3
æ
represents
the
largest
integer
that
is
≤
n/
3.
The
signal
x
[
n
] is
plotted
below.
Enter
a
closedform
expression
for
X
(
z
) in
the
box
below.
X
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 Spring '11
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