EECS 20N: Structure and Interpretation of Signals and Systems
Department of Electrical Engineering and Computer Sciences
U
NIVERSITY OF
C
ALIFORNIA
B
ERKELEY
Final Exam Sol.
13 December 2005
LAST Name
FOURIER
FIRST Name
Jean Baptiste Joseph
Lab Time
365/24/7
•
(10 Points)
Please print your name and lab time in legible, block lettering
above, and on the back of the last page.
•
This exam should take you about two hours to complete. However, you will
be given up to about three hours to work on it.
We recommend that you
budget your time as a function of the point allocation and difficulty level (for
you) of each problem or modular portion thereof.
•
This exam printout consists of pages numbered 1 through 14.
Also in
cluded is a doublesided appendix sheet containing transform properties.
When you are prompted by the teaching staff to begin work, verify that your
copy of the exam is free of printing anomalies and contains all of the fourteen
numbered pages and the appendix. If you find a defect in your copy, notify
the staff immediately.
•
This exam is closed book.
Collaboration is not permitted.
You may not
use or access, or cause to be used or accessed, any reference in print or elec
tronic form at any time during the quiz. Computing, communication, and
other electronic devices (except dedicated timekeepers) must be turned off.
Noncompliance with these or other instructions from the teaching staff—
including, for example, commencing work prematurely or continuing beyond the
announced stop time
—is a serious violation of the Code of Student Conduct.
•
Please write neatly and legibly, because
if we can’t read it, we can’t grade it.
•
For each problem, limit your work to the space provided specifically for that
problem.
No other work will be considered in grading your exam. No exceptions.
•
Unless explicitly waived by the specific wording of a problem, to receive full
credit, you must explain your responses succinctly, but clearly and convinc
ingly.
•
We hope you do a
fantastic
job on this exam.
•
It has been a pleasure having you in EECS 20N. Happy holidays!
1
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•
Complex exponential Fourier series synthesis and analysis equations for a
periodic discretetime signal having period
p
:
x
(
n
) =
X
k
=
h
p
i
X
k
e
ikω
0
n
←→
X
k
=
1
p
X
n
=
h
p
i
x
(
n
)
e

ikω
0
n
,
where
p
=
2
π
ω
0
and
h
p
i
denotes a suitable contiguous discrete interval of length
p
(for example,
X
k
=
h
p
i
can denote
p

1
X
k
=0
).
•
Complex exponential Fourier series synthesis and analysis equations for a
periodic continuoustime signal having period
p
:
x
(
t
) =
∞
X
k
=
∞
X
k
e
ikω
0
t
←→
X
k
=
1
p
Z
h
p
i
x
(
t
)
e

ikω
0
t
dt ,
where
p
=
2
π
ω
0
and
h
p
i
denotes a suitable continuous interval of length
p
(for
example,
Z
h
p
i
can denote
Z
p
0
).
•
Discretetime Fourier transform (DTFT) synthesis and analysis equations for
a discretetime signal:
x
(
n
) =
1
2
π
Z
h
2
π
i
X
(
ω
)
e
iωn
dω
←→
X
(
ω
) =
∞
X
n
=
∞
x
(
n
)
e

iωn
,
where
h
2
π
i
denotes a suitable continuous interval of length
2
π
(for example,
Z
h
2
π
i
can denote
Z
2
π
0
or
Z
π

π
).
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 Spring '08
 EdwardA.Lee
 Electrical Engineering, Fourier Series, wf wf wf, NWF NWF NWF, Machine C WF WF WF WF NWF NWF NWF NWF

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