STUDY UNIT 2
Analysis of Communication Signals
1.1 LEARNING OUTCOMES
After working through this study unit, you should be able to
• Identify time-domain properties of a signal from its frequency-domain
representation and vice-versa.
• Model signals mathematically using mathematical expressions, vectors or phasors.
• Determine Fourier series and Fourier transforms of repetitive signals.
• Use transform theorems to determine and sketch the spectrum of a signal defined
by time-domain operations.
• Identify time-domain properties of a signal from its frequency-domain
representation and vice-versa.
1.2 INTRODUCTION
As discussed in study unit 1, telecommunication consists of information from a source to a
destination over a long distance. The information being exchanged between the source and
the destination through the communication channel is modelled as a signal.
A signal refers to the variation of a physical quantity with respect to time. For example,
temperature in a room varies as time elapses. Voltage and current are electrical signals which
are used in telecommunication to convey information.
In this study unit, you will be introduced to the concept of a signal as a function that
represents a physical quantity. Mathematical representation of a signal will be discussed,
starting with a signal as a function of time. This will be called a time domain representation.
Then we shall move on to introduce another domain representation of a signal called the
, frequency domain. This knowledge will be used later to obtain more information about a
signal. Another form of signal representation is introduced, called phasor representation, as
we prepare the reader for the frequency domain representation. Then manipulation of signals
as an odd and even representation will be given. Eventually, different types of signals and
their representation in both frequency and time domains will be given to allow the reader to
practice converting a signal from time to frequency domain and vice versa. Both Fourier
series and Fourier transforms will be introduced as tools to represent signals. A good
understanding of these tools will help you to determine and sketch the spectrum of a signal
defined by time-domain operations.
1.3 INTRODUCTION TO SIGNALS
A signal is a function representing a physical quantity or variable. It is a representation of
data. It contains information about the behavior or nature of a phenomenon, hence it can be
any sign, gesture, token, etc. that serves to communicate information. An example could be
voltage (voltage signal) which itself may convey the content of speech, and image or data,
etc. Mathematically, a signal is represented as a function of an independent variable, usually
time, t. Since a signal is a function, it is represented by the symbols used for mathematical
functions, x(t) or f(t), where x or f is the dependent variable (e.g. voltage, sound pressure,
flow rate) and can be expressed as a mathematical expression, e.g. x(t)=t or f(t)=t. This
means that a function x associates with every number t, another number x(t) which is called
the value of the function at t. This association can also be represented pictorially by a graph
as shown below
x(t)
0 t
The mathematical representation of signals helps us understand the various processes that
affect signals in their passage through systems such as telecommunication networks. An
example of a signal is a speech signal. The diagram below shows a waveform of a speech
signal through a cellular phone system
sound sound
in out
Cellphone
System t
t
Since signals are mathematical functions, they may have one independent variable (1D signal),
, or two independent variables (2D signal), or three (3D), or m (m-dimensional signal). That is, a
signal that is represented as a collection of m variables is referred to as an m-dimensional
signal.
Various types of signals are used to convey information in a telecommunication system. The
main signals include:
• Audio signal (voice): this is a 1D representation of sound signal as picked up by a
microphone transducer, typically using either a changing level of electrical voltage for
analog signals, or a series of binary numbers for digital signals. This category caters for
voice calls (telephone and cellphone voice calls), radio, voice over IP (through the
Internet such as WhatsApp calls etc.)
• Text signals: These are 1D digital electrical signals that encode written text signals
using many encoding mechanisms such as the ASCII code, as studied in digital
electronics, on the transmitter side. The transmitted electrically encoded text messages
are decoded on the receiver side. This category includes SMS (Short Message Service),
text chat messages etc.
• Images: These are 2D signals has a signal point as an (x, y) coordinate e.g., brightness
b (x, y). The dependent variable can be a scalar or vector. Scalar: brightness at each
point (x, y). Vector: color (red, green, blue) at each point (x, y). Images are exchanged
through various telecommunication systems such as the television system (analogue
and digital), MMS (Multimedia Messaging Service) which allows the exchange of
images between the source and destination in a telecommunication system, social
image messages via WhatsApp etc.
• Videos: These are 2D, 3D and even 4D signals that consist of a sequence of image
signals acquired at different rates expressed in terms of frames per second. Video
signals are exchanged through telecommunication systems such as the television
system (analogue and digital), MMS, social media video calls, conference calls, Internet
video streaming (YouTube etc.).
ACTIVITY 1
1. Given the following sound signal:
Using the MATLAB simulator, use the “waveread()” function, read and plot the sound signal
in time domain. Label all axes.
2. Using MATLAB, represent the digital electrical signal that will be sent from a digital processor
to a radio transmitter, if the text message “Hi” encoded using the ASCII scheme at TTL
voltage level. Label all axes.
3. Using the MATLAB functions “imread()” and “image()” , read and plot and label all axes,
for the image signal below:
sample_image.png
4. Using the MATALB functions “VideoReader()” , “hasFrame()”, “readFrame()”and
“image()”, read and play the images of the following video signal.
Analysis of Communication Signals
1.1 LEARNING OUTCOMES
After working through this study unit, you should be able to
• Identify time-domain properties of a signal from its frequency-domain
representation and vice-versa.
• Model signals mathematically using mathematical expressions, vectors or phasors.
• Determine Fourier series and Fourier transforms of repetitive signals.
• Use transform theorems to determine and sketch the spectrum of a signal defined
by time-domain operations.
• Identify time-domain properties of a signal from its frequency-domain
representation and vice-versa.
1.2 INTRODUCTION
As discussed in study unit 1, telecommunication consists of information from a source to a
destination over a long distance. The information being exchanged between the source and
the destination through the communication channel is modelled as a signal.
A signal refers to the variation of a physical quantity with respect to time. For example,
temperature in a room varies as time elapses. Voltage and current are electrical signals which
are used in telecommunication to convey information.
In this study unit, you will be introduced to the concept of a signal as a function that
represents a physical quantity. Mathematical representation of a signal will be discussed,
starting with a signal as a function of time. This will be called a time domain representation.
Then we shall move on to introduce another domain representation of a signal called the
, frequency domain. This knowledge will be used later to obtain more information about a
signal. Another form of signal representation is introduced, called phasor representation, as
we prepare the reader for the frequency domain representation. Then manipulation of signals
as an odd and even representation will be given. Eventually, different types of signals and
their representation in both frequency and time domains will be given to allow the reader to
practice converting a signal from time to frequency domain and vice versa. Both Fourier
series and Fourier transforms will be introduced as tools to represent signals. A good
understanding of these tools will help you to determine and sketch the spectrum of a signal
defined by time-domain operations.
1.3 INTRODUCTION TO SIGNALS
A signal is a function representing a physical quantity or variable. It is a representation of
data. It contains information about the behavior or nature of a phenomenon, hence it can be
any sign, gesture, token, etc. that serves to communicate information. An example could be
voltage (voltage signal) which itself may convey the content of speech, and image or data,
etc. Mathematically, a signal is represented as a function of an independent variable, usually
time, t. Since a signal is a function, it is represented by the symbols used for mathematical
functions, x(t) or f(t), where x or f is the dependent variable (e.g. voltage, sound pressure,
flow rate) and can be expressed as a mathematical expression, e.g. x(t)=t or f(t)=t. This
means that a function x associates with every number t, another number x(t) which is called
the value of the function at t. This association can also be represented pictorially by a graph
as shown below
x(t)
0 t
The mathematical representation of signals helps us understand the various processes that
affect signals in their passage through systems such as telecommunication networks. An
example of a signal is a speech signal. The diagram below shows a waveform of a speech
signal through a cellular phone system
sound sound
in out
Cellphone
System t
t
Since signals are mathematical functions, they may have one independent variable (1D signal),
, or two independent variables (2D signal), or three (3D), or m (m-dimensional signal). That is, a
signal that is represented as a collection of m variables is referred to as an m-dimensional
signal.
Various types of signals are used to convey information in a telecommunication system. The
main signals include:
• Audio signal (voice): this is a 1D representation of sound signal as picked up by a
microphone transducer, typically using either a changing level of electrical voltage for
analog signals, or a series of binary numbers for digital signals. This category caters for
voice calls (telephone and cellphone voice calls), radio, voice over IP (through the
Internet such as WhatsApp calls etc.)
• Text signals: These are 1D digital electrical signals that encode written text signals
using many encoding mechanisms such as the ASCII code, as studied in digital
electronics, on the transmitter side. The transmitted electrically encoded text messages
are decoded on the receiver side. This category includes SMS (Short Message Service),
text chat messages etc.
• Images: These are 2D signals has a signal point as an (x, y) coordinate e.g., brightness
b (x, y). The dependent variable can be a scalar or vector. Scalar: brightness at each
point (x, y). Vector: color (red, green, blue) at each point (x, y). Images are exchanged
through various telecommunication systems such as the television system (analogue
and digital), MMS (Multimedia Messaging Service) which allows the exchange of
images between the source and destination in a telecommunication system, social
image messages via WhatsApp etc.
• Videos: These are 2D, 3D and even 4D signals that consist of a sequence of image
signals acquired at different rates expressed in terms of frames per second. Video
signals are exchanged through telecommunication systems such as the television
system (analogue and digital), MMS, social media video calls, conference calls, Internet
video streaming (YouTube etc.).
ACTIVITY 1
1. Given the following sound signal:
Using the MATLAB simulator, use the “waveread()” function, read and plot the sound signal
in time domain. Label all axes.
2. Using MATLAB, represent the digital electrical signal that will be sent from a digital processor
to a radio transmitter, if the text message “Hi” encoded using the ASCII scheme at TTL
voltage level. Label all axes.
3. Using the MATLAB functions “imread()” and “image()” , read and plot and label all axes,
for the image signal below:
sample_image.png
4. Using the MATALB functions “VideoReader()” , “hasFrame()”, “readFrame()”and
“image()”, read and play the images of the following video signal.
