EECS 20N: Structure and Interpretation of Signals and Systems
Department of EECS
University of California Berkeley
Problem Set 4
Issued: 10 October 2008
Due: 17 October 2008, 5pm
The Absolute Necessity of Seeking Inspiration in Nature
We may learn a great deal from books, but we learn much more from
the contemplation of nature—the reason and occasion for all books.
The direct examination of phenomena has an indescribably disturbing
and leavening effect on our mental inertia—a certain exciting and re
vitalizing quality altogether absent, or barely perceptible, in even the
most faithful copies and descriptions of reality.
a
a
Excerpts from
Advice for a Young Investigator
, by Santiago Ram´on y
Cajal, translated by Neely Swanson and Larry W. Swanson, The MIT Press,
1999, ISBN: 0262681501.
Policy Statement
•
You are encouraged to collaborate, but only in a group of up to
five
current
EECS 20N students.
•
On the solution document that you turn in for grading, you must write the
names of your collaborators below your own; each teammate must submit for
our evaluation a distinct, selfprepared solution document containing original
contributions to the collaborative effort.
•
Please write neatly and legibly, because
if we can’t read it, we can’t grade it.
•
Unless we explicitly state otherwise, you will receive full credit
only if
you explain
your work succinctly, but clearly and convincingly.
•
Typically, we evaluate your solutions for only a subset of the assigned problems.
A priori, you do not know which subset we will grade. It is to your advantage to
make a bona fide effort at tackling
every
assigned problem.
•
If you are asked to provide a ”sketch,” it refers to a
handdrawn
sketch, well
labeled to indicate all the salient features—not a plot generated by a computing
device.
1
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Overview, Subject Matter, and Reading
This problem set explores some of the salient properties of discretetime convolution
and frequency responses of discretetime systems. It also covers some of the salient
properties of the Dirac delta. You should read all of the material in Chapters 8 and 9
of the textbook (Lee & Varaiya).
HW4.1 (Impulse Response and Step Response of DTLTI Systems)
The discrete
time unitimpulse signal
δ
, characterized by the Kronecker delta function
δ
(
n
) =
(
1
n
= 0
0
n
6
= 0
,
is applied to a discretetime linear timeinvariant (DTLTI) system. The corresponding
output signal
h
is called the
impulse response
of the system.
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 Spring '08
 BabakAyazifar
 Digital Signal Processing, LTI system theory, Impulse response, Dirac delta function, Dirac delta

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