EE1205 Introduction to electrical engineering
The University of Texas at Arlington
Compiled by Md.
Raziul
Hasan
Revised
and amended
by K. Alavi
Sign

> Signal
•
Traffic
signal
•
Flashing indicator light of a car
•
Mobile network signal
•
In the fields of communications, signal processing,
and in electrical engineering more generally, a
signal
is any time

varying or spatial

varying quantity.
ref:
http://en.wikibooks.org/wiki/Signals_and_Systems/Definition_of_Signals_and_Systems
•
"A signal is a function of
independent
variables that
carry some information
.“
•
e.g. A Voltage V(t) or a Current C(t) that depends
on time
t
V
(
t
)
•
Three ways to represent a complex number
•
cartesian
z=
x+iy
•
polar
•
Exponential
z=r
e
i
φ
•
z r
2 2
r x y and in radians
•
Euler's
formula:
e
i
φ
=
cos
φ
+
i
sin
φ
Then x=
cos
φ
and y= sin
φ
And x=Re {
e
i
φ
} and y=
Im
{
e
i
φ
}
Let
φ
=
ω
t
+
Then
x
=Re{
e
i
ω
t
+
}=
cos
(
ω
t
+
)
And y
=
Im
{
e
i
ω
t
+
}=sin(
ω
t
+
)
y
= sin(
ω
t
+
) =
Im
{
e
i
(
ω
t
+
)
}
•
Mathematically, signals are represented as a
function of one or more
independent variables
.
•
Below signal
depends on
independent variable
t
with parameters A,
ω
and
.
•
s
=
A
Sin(
ω
t
+
)=A
Im
{
e
j
(
ω
t
+
)
}
A=Amplitude real
ω
=angular frequency
=phase
Sin( ~ )=function
ref: http
://radarproblems.com/chapters/ch05.dir/ch05pr.dir/c05p1.dir/c05p1.htm
Analog and digital
signals
Continuous and
Discrete

Time
Signals
Periodic aperiodic Signal
•
Unit
Step Function u(t
)
•
Ramp
function r(t)
•
A
System
is any physical set of components that
takes a
signal
and
transforms it into another
signal.
•
A system can be a simple one that turns a light
ON/OFF. Or can be a complex one that does all
the computation in a microprocessor.
ref
: http://www.dreamstime.com/royalty

free

stock

image

microchip

circuit

image12540796
System
Input signal x(t)
Output signal y(t)
•
An
electronic amplifier
is a device for increasing the
power of a signal
.
•
It
does this by taking energy from a power supply
and controlling the output to match the input signal
shape but with a larger amplitude.
•
There are various types of amplifier.
Amplifier
•
A time shifter system shifts the function f(t) forward
or backward by a specific time.
•
The above system is a forward time shifter. It adds a
delay (t
0)
to the signal.
t
t
Time shifter
f
(t)
f(t
–
t
0
)
•
sampling
is the reduction of a
continuous

time
signal to a
discrete

time signal
•
The sampling frequency must be higher than the
frequency of the signal to be sampled. (minimum
twice as high)
Sampler
ref: http
://en.wikipedia.org/wiki/Sampling_%28signal_processing%29
•
An
analog

to

digital converter
(
ADC
,
A/D
)
is a
device that converts a continuous quantity to a
discrete time digital representation
.
•
The system that does the opposite is called
DAC
Analog to
Digital
ref: http
://pictureofgoodelectroniccircuit.blogspot.com/2010/04/phase

and

function

of

analog

signal

or.html
DAC
•
Conversion of Analog to digital is done in two step.
1.
Continuous analog
卡浰汥搠獩杮慬
㈮
卡浰汥搠獩杮慬s
兵慮瑩穥搠摩杩瑡氠獩杮慬
A/D
Sampler
ref: http
://en.wikipedia.org/wiki/Quantization_%
28signal_processing%29
•
A low

pass filter is a filter that passes low

frequency
signals but attenuates (reduces the amplitude of)
signals with frequencies higher than the cutoff
frequency.
ref:
http://en.wikipedia.org/wiki/Low

pass_filter
Low Pass
Filter
0
20
40
60
80
100
120
140
160
180
200
1
0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
0
20
40
60
80
100
120
140
160
180
200
0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
•
A high

pass filter (HPF) is a device that passes high
frequencies and attenuates (i.e., reduces the
amplitude of) frequencies lower than its cutoff
frequency.
ref:
http://
en.wikipedia.org/wiki/High

pass_filter
Low Pass
Filter
0
20
40
60
80
100
120
140
160
180
200
0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
0
20
40
60
80
100
120
140
160
180
200
1
0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
•
A band

pass filter is a device that passes
frequencies within a certain range and rejects
(attenuates) frequencies outside that range.
ref:
http://
en.wikipedia.org/wiki/Band

pass_filter
Band Pass
Filter
0
20
40
60
80
100
120
140
160
180
200
1
0
1
2
3
4
5
6
7
0
20
40
60
80
100
120
140
160
180
200
0.5
0
0.5
1
1.5
2
2.5
3
3.5
•
band

stop filter or band

rejection filter is a filter that
passes most frequencies unaltered, but attenuates
those in a specific range to very low levels
ref:
http://
en.wikipedia.org/wiki/Band

stop_filter
Band
–
stop
Filter
0
20
40
60
80
100
120
140
160
180
200
1
0
1
2
3
4
5
6
7
0
20
40
60
80
100
120
140
160
180
200
1
0
1
2
3
4
5
•
In signal processing, sampling is
the reduction of a continuous
signal to a discrete
signal.
•
Sampling frequency defines the
sampling ‘
RESOLUTION
’
ref: http
://en.wikipedia.org/wiki/Sampling_%
28signal_processing%29,
http
://fourier.eng.hmc.edu/e101/lectures/Sampling_theorem/node1.html
•
Fourier
Series expansion:
ref:
http
://mathworld.wolfram.com/FourierSeries.html
The first four Fourier series
approximations for a square
wave.
•
A periodic square
wave function
ƒ
(
x
)
can be expressed
with infinite Fourier
series expansion.
f(x)
=sin(x)+
1
3
sin(3x)+
1
5
sin(5x)+
1
7
sin(7x)+…..
ref
: http://www.intmath.com/fourier

series/2

full

range

fourier

series.php
Figure: Construction of
a square wave from
sinusoids of different frequencies
•
Communication Applications:
Transmission of information (signal) over a channel
“Modulation”
•
Control Applications:
Control
the speed of fan
•
Signal
Processing
Applications:
o
Speech and audio processing
o
Multimedia processing
•
Biological Signal
Analysis:
o
Brain signals (EEG)
o
Cardiac signals (ECG)
o
Medical images (x

ray, PET, MRI)
ref: http
://
images.yourdictionary.com/amplitude

modulation,
http
://en.wikipedia.org/wiki/Amplitude_modulation
•
An Amplitude modulator takes a low frequency
message signal and a high frequency carrier
signal and combines it into a modulated signal of
varying amplitude.
ref:
http://encyclopedia2.thefreedictionary.com/Amplitude+Modulation
Amplitude
Modulator
•
An
Amplitude demodulator
takes a modulated
signal as input and gives output the original
message signal.
•
The above system is an amplitude demodulator.
Its also called
‘envelope detector’.
It takes the
envelope of the modulated signal to get the
information signal.
ref:
http://encyclopedia2.thefreedictionary.com/Amplitude+Modulation
Amplitude
Demodulator
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