EEC
E
151
:
Introductio
n
t
o
ECE Laborator
y
Laboratory 2:
Introductio
n
t
o
Digita
l
Signa
l
Processin
g
an
d
Communication
s
Description:
Thi
s
week’
s
exercise
s
wil
l
provid
e
yo
u
wit
h
a
n
introductor
y
understandin
g
o
f
signa
l
processin
g
(i
n
particular
,
digita
l
signa
l
processing
,
o
r
DSP
)
an
d
wha
t
i
t
i
s
use
d
for
.
Yo
u
wil
l
als
o
b
e
introduce
d
t
o
som
e
basi
c
idea
s
o
f
digita
l
communications
.
Th
e
la
b
consist
s
o
f a
compute
r
experimen
t
wit
h a
wireles
s
acousti
c
modem
.
Prelab:
Read through Sections 1 through 3 and put summary notes in your lab
notebook.
Ther
e
i
s
considerabl
e
informatio
n
t
o
rea
d
befor
e
yo
u
com
e
int
o
th
e
lab
,
s
o
b
e
sur
e
t
o
allo
t
yoursel
f
enoug
h
tim
e
t
o
full
y
prepar
e
fo
r
th
e
la
b
thi
s
week
.
You
r
notebook
s
wil
l
b
e
checke
d
a
t
th
e
beginnin
g
o
f
clas
s
t
o
ensur
e
tha
t
you
r
prela
b
ha
s
bee
n
completed
.
Yo
u
shoul
d
als
o
rea
d
throug
h
th
e
remainin
g
section
s
t
o
b
e
prepare
d
fo
r
lab
.
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1
t
Figure 1: An example of an analog, or continuoustime, signal.
Introduction
Let’s begin with some basic definitions. A
signal
can be thought of as anything that bears infor
mation in which we are interested.
Examples include audio signals such as someone honking to
get your attention or someone speaking to give you directions, and the light signals at a traﬃc
light which indicate if you can proceed through an intersection or need to stop.
Signal processing
describes the process of manipulating signals to produce some desired result or to gather some
information.
An
analog
, or continuoustime signal, can take on any real value at any time
t
, as
illustrated in Fig. 1. Most realworld signals exist only in analog form. A
discretetime
signal can
only take on values at discrete times,
t
=
kT
, where
T
is a fixed positive real number and
k
is an
integer. A discretetime version of the analog signal in Fig. 1 is shown in Fig. 2. The discretetime
signal can be obtained by “sampling” the original analog signal at the discrete time points
t
=
kT
,
where 1
/T
is called the “sampling rate”.
Note that the process of sampling involves discarding
an infinite amount of data (i.e., all of the signal values between the sample points).
Thus, one
would intuitively reason that the original analog signal could not be recovered completely from
the discretetime signal.
However, a fundamental result of digital signal processing proved that
if the sampling rate is chosen appropriately, then the analog can be recreated
exactly
from the
discretetime signal. This is key to the modern advances in digital audio and video technologies.
The discrete sample points provide a finite set of signal values over a finite time interval
(i.e., a fixed number of samples), unlike the analog signal. Thus, it is more suited for processing
digitally, i.e., on a computer which uses a fixed (finite) set of numbers by using a fixed number of
bits (0s and 1s) to represent data. Since each sample of the discretetime signal can take on an
infinite number of values, they cannot be represented by a finite number of bits in a computer.
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 Fall '08
 Heikenfield
 signal constellation

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