CHAPTER THREE

Signals

Unit Structure
2.0 Objectives
2.1 Introduction
2.2 Data & Signals
2.2.1 Data –types
2.2.2 Signal – types
2.2.3 Periodic & Non Periodic Signals
2.3 Analog Signal
2.3.1 Characteristics of Analog Signal
2.3.1.1 Peak Amplitude
2.3.1.2 Frequency
2.3.1.3 Phase
2.3.2 Relation between Frequency & Period
2.3.3 Wavelength
2.3.4 Time & Frequency Domain Representation of a signal
2.3.5 Composite Signal
2.4 Digital Signal
2.4.1 Definition
2.4.2 Level
2.4.3 Bit lenght or Bit Interval
2.4.4 Bit Rate
2.4.5 Baud Rate
2.5 Types of Channel
2.5.1 Lowpass Channel
2.5.2 Bandpass Channel
2.6 Transmission of Digital signal
2.6.1 Baseband Transmission
2.6.2 Broadband Transmission
2.7 Review Questions
2.8 References
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2.0 OBJECTIVES

 Introduce the readers to fundamentals of data & signal

 Types of data & signal
 Characteristics and nature of analog & digital signal
 Representation of signal
 Transmission of digital signals

2.1 INTRODUCTION

Computer networks are designed to transfer data from one

point to another. During transit data is in the form of
electromagnetic signals. Hence it is important to study data and
signals before we move to further concepts in data communication.

2.2 DATA & SIGNALS

To be transmitted, data must be transformed to

electromagnetic signals.

2.2.1. Data can be Analog or Digital.

1. Analog data refers to information that is continuous; ex.

sounds made by a human voice
2. Digital data refers to information that has discrete states.
Digital data take on discrete values.
3. For example, data are stored in computer memory in the
form of Os and 1s

2.2.2. Signals can be of two types:

1. Analog Signal: They have infinite values in a range.
2. Digital Signal: They have limited number of defined
values

Figure: a. Analog Signal b. Digital Signal*

2.2.3. Periodic & Non Periodic Signals
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Signals which repeat itself after a fixed time period are called
Periodic Signals.
Signals which do not repeat itself after a fixed time period
are called Non-Periodic Signals.
In data communications, we commonly use periodic
analog signals and non-periodic digital signals.

2.3 ANALOG SIGNAL

An analog signal has infinitely many levels of intensity over a

period of time.
As the wave moves from value A to value B, it passes
through and includes an infinite number of values along its
path as it can be seen in the figure below.
A simple analog signal is a sine wave that cannot be further
decomposed into simpler signals.

Fig. Sine wave

A sine wave is characterized by three parameters:

1. Peak Amplitude
2. Frequency
3. Phase

2.3.1 Characteristics of an Analog Signal

2.3.1.1 Peak Amplitude

The amplitude of a signal is the absolute value of its
intensity at time t
The peak amplitude of a signal is the absolute value of
the highest intensity.
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The amplitude of a signal is proportional to the energy

carried by the signal

Fig. Amplitude of a sine wave

2.3.1.2. Frequency
Frequency refers to the number of cycles completed by the
wave in one second.
Period refers to the time taken by the wave to complete one
second.

Fig: Frequency & Period of a sine wave

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2.3.1.3. Phase
Phase describes the position of the waveform with respect to time
(specifically relative to time O).

Fig: Phase of a sine wave*

Phase indicates the forward or backward shift of the

waveform from the axis
It is measured in degrees or radian
The figure above shows the sine waves with same amplitude
and frequency but different phases

2.3.2 Relation between Frequency & Period

Frequency & Period are inverse of each other.

It is indicated by the following formula:
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Example1. A wave has a frequency of 100hz. Its period(T) is given

by
T = 1/ F = 1/ 100 = 0.01 sec

Example2. A wave completes its one cycle in 0.25 seconds. Its

frequency is given by
F = 1 / T = 1 / 0.25 = 4 Hz

2.3.3 Wavelength
The wavelength of a signal refers to the relationship between
frequency (or period) and propagation speed of the wave
through a medium.
The wavelength is the distance a signal travels in one
period.
It is given by
Wavelength = Propagation Speed X Period
OR
Wavelength =Propagation Speed X 1 a
Frequency
It is represented by the symbol : λ (pronounced as lamda)
It is measured in micrometers
It varies from one medium to another.

2.3.4. Time Domain and Frequency domain representation of

signals

A sine wave can be represented either in the time domain or

frequency domain.
The time-domain plot shows changes in signal amplitude
with respect to time. It indicates time and amplitude relation
of a signal.
The frequency-domain plot shows signal frequency and
peak amplitude.
The figure below show time and frequency domain plots of
three sine waves.
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Fig: Time domain and frequency domain plots of three sine

waves*

A complete sine wave in the time domain can be

represented by one single spike in the frequency domain

2.3.5. Composite Signal

A composite signal is a combination of two or more simple
sine waves with different frequency, phase and amplitude.
If the composite signal is periodic, the decomposition gives a
series of signals with discrete frequencies; if the composite
signal is non-periodic, the decomposition gives a
combination of sine waves with continuous frequencies.

Fig: A Composite signal with three component signals

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For data communication a simple sine wave is not useful,

what is used is a composite signal which is a combination of
many simple sine waves.

According to French Mathematician, Jean Baptist, any

composite signal is a combination of simple sine waves with
different amplitudes and frequencies and phases.

Composite signals can be periodic or non periodic.

A periodic composite signal can be decomposed into a

series of signals with discrete frequencies.

A non-periodic signal when decomposed gives a

combination of sine waves with continuous frequencies.

Fig The time and frequency domains of a non-periodic

composite analog signal

2.4 Digital Signal

Information can also be explained in the form of a digital
signal.
A digital signal can be explained with the help of following
points:

2.4.1 Definition:-
A digital is a signal that has discrete values.
The signal will have value that is not continuous.

2.4.2 LEVEL
Information in a digital signal can be represented in the
form of voltage levels.
Ex. In the signal shown below, a ‗1‘ is represented by a
positive voltage and a ‗0‘ is represented by a Zero voltage.
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Fig: A digital signal with Two levels. „1‟ represented by a

positive voltage and „0‟ represented by a negative voltage
A Signal can have more than two levels

11 10 01 00 00 01 10 10
LEVEL
4
LEVEL
3
LEVEL
2
LEVEL
1

Fig: A digital signal with four levels

In general, if a signal has L levels then, each level need
Log2L bits
Example: Consider a digital Signal with four levels, how
many bits are required per level?
Answer: Number of bits per level = Log2L
= Log24
=2
Hence, 2 bits are required per level for a signal with four
levels.
2.4.3 BIT LENGTH or Bit Interval (Tb)
It is the time required to send one bit.
It is measured in seconds.
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2.4.4 BIT RATE

It is the number of bits transmitted in one second.
It is expressed as bits per second (bps).
Relation between bit rate and bit interval can be as follows
Bit rate = 1 / Bit interval

2.4.5 Baud Rate

It is the rate of Signal Speed, i.e the rate at which the signal
changes.
A digital signal with two levels ‗0‘ & ‗1‘ will have the same
baud rate and bit rate & bit rate.
The diagram below shows three signal of period (T) 1
second
a) Signal with a bit rate of 8 bits/ sec and baud rate of 8
baud/sec
b) Signal with a bit rate of 16 bits/ sec and baud rate of 8
baud/sec
c) Signal with a bit rate of 16 bits/ sec and baud rate of 4
baud/sec

Fig: Three signals with different bit rates and baud rates
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2.5 TYPES OF CHANNELS:

Each composite signal has a lowest possible(minimum)

frequency and a highest possible (maximum) frequency.

From the point of view of transmission, there are two types of

channels:

2.5.1 Low pass Channel

This channel has the lowest frequency as ‗0‘ and highest
frequency as some non-zero frequency ‗f1‘.
This channel can pass all the frequencies in the range 0 to f1.

2.5.2 Band pass channel

This channel has the lowest frequency as some non-zero
frequency ‗f1‘ and highest frequency as some non-zero
frequency ‗f2‘.
This channel can pass all the frequencies in the range f1 to f2.

Fig: Lowpass Channel & Bandpass Channel

2.6 Transmission of Digital signal

Digital signal can be transmitted in the following two ways:

2.6.1 Baseband Transmission

The signal is transmitted without making any change to it
(ie. Without modulation)
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In baseband transmission, the bandwidth of the signal to

be transmitted has to be less than the bandwidth of the
channel.

Ex. Consider a Baseband channel with lower frequency

0Hz and higher frequency 100Hz, hence its bandwidth is
100 (Bandwidth is calculated by getting the difference
between the highest and lowest frequency).

We can easily transmit a signal with frequency below

100Hz, such a channel whose bandwidth is more than
the bandwidth of the signal is called Wideband channel

Logically a signal with frequency say 120Hz will be

blocked resulting in loss of information, such a channel
whose bandwidth is less than the bandwidth of the signal
is called Narrowband channel

2.6.2 Broad band Transmission

Given a bandpass channel, a digital signal cannot be
transmitted directly through it

In broadband transmission we use modulation, i.e we

change the signal to analog signal before transmitting it.

The digital signal is first converted to an analog signal,

since we have a bandpass channel we cannot directly
send this signal through the available channel. Ex.
Consider the bandpass channel with lower frequency
50Hz and higher frequency 80Hz, and the signal to be
transmitted has frequency 10Hz.

To pass the analog signal through the bandpass channel,

the signal is modulated using a carrier frequency. Ex.
The analog signal (10Hz) is modulated by a carrier
frequency of 50Hz resulting in an signal of frequency
60Hz which can pass through our bandpass channel.

The signal is demodulated and again converted into an

digital signal at the other end as shown in the figure
below.
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Fig: Broadband Transmission Involving Modulation &

Demodulation

2.7 REVIEW QUESTIONS

1. Define analog and digital signals

2. Explain Composite analog signals.
3. Explain Time and Frequency Domain Representation of
signals
4. Explain the characteristics of an Analog signal
5. Explain the characteristics of an Digital signal
6. Explain the difference between
1. Lowpass and Bandpass channel
2. Narrowband and wideband channel
7. Explain why a digital signal requires to undergo a change
before transmitting it through a bandpass channel.

2.8 REFERENCES & FURTHER READING

Data Communication & Networking – Behrouz Forouzan

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