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Homework 1 (ECE220  Fall 2007)
•
Due:
Thursday, September 6 at the beginning of lecture.
•
Reasoning and work must be shown to gain full/partial credit.
•
WRITE YOUR NAME AND NET ID ON ALL PAGES HANDED IN!
1.
(20 points) Premise
You are familiar with the concept of variable. Signals are a more
sophisticated mathematical objects that extend the static concept of variable in order
to capture a variable that changes dynamically. It may evolve in time, space, or with
respect to some other, ehm, variable. Conventionally one refers to the dimensions of the
independent variable, for example, time is 1D (onedimensional), space can be 2D in
an image or 3D in actuality, when specifying what kind of signal we are dealing with.
A 3D signal is a video, which is a set of images evolving with time. This is not referring
to the signal itself, which if studied as a vector, lies in a space usually with a great deal
of more dimensions than its index.
(20 points) There are two classes of signals. The ones that we commonly experience
ﬁt best the abstraction of
analog signals
. A 1D analog signal is denoted for ex
ample as
s
(
t
) :
s
(
t
)
∈
R
or
∈
C
and
t
∈
R
. An analog image signal would be:
s
(
x,y
) :
s
(
x,y
)
∈
R
or
∈
C
and
x,y
∈
R
. The deﬁnition can be clearly extended to
multidimensional signals
s
(
x
1
,...,x
n
) where, (
x
1
,...,x
n
)
∈
R
n
. Also, the signal itself
sometimes takes only discrete values, which is an obvious special case.
Digital signals
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 Fall '05
 JOHNSON

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