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

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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

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

(
,
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

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