Communication and Networks Assignment
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Diploma in Information Technology
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Lesson 7: Analogue and Digital Signals
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Lesson 7 Learning Outcomes
Distinguish between analogue and digital signal
Distinguish between periodic and aperiodic signals
Define sine waves
Identify the four important characteristics of signals
Define composite signals
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Lesson 7 Learning Outcomes
Discuss the time and frequency domain representation of signals
Use Shannon law and Nyquist theorem to calculate the channel theoretical capacity
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Lesson 7 Outline
Data Communications
Communication Model
Physics of Transmission
Types of Signal
Representing Signals
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Information Source & Destination
Communication system accepts input from one or more sources and delivers to a destination
On the Internet, source and destination of information are pair of application programs
Source: generate data
Destination: consume data
Source: Bing, licensed under CC BY-SA
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Data Communications
Data communications theory concentrates on low-level communications systems
Sources: microphones, sensors, measuring devices like thermometers and scales and computer peripherals like keyboards, mice
Destinations: audio output devices like earphones and loud-speakers, LEDs that emit light
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Data vs Computer Communications
In most cases, the terms are interchangeable
To be specific:
Data communication: for lower layer aspects like signaling, device interfaces, hardware related issues
Computer communication: for higher layer aspects such as network protocols, applications, software related issues
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Communication Model
Provides an understanding of how information is transferred
Shows how information is sent and received
Shows the parties and factors involved in a communication
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Claude Shannon & Warren Weaver
In 1948, Shannon and Weaver came up with an idea
Successful communication requires:
Information source: generates data
Messages: data transmitted
Transmitter: converts information to signals
Channel: medium in which signal are transmitted
Receiver: translate signal back to original message
Destination: consume data
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Shannon’s Communications Model
Information
Source
Transmitter
Channel
Receiver
Destination
Noise Source
Noise
Message
Signal
Received Signal
Message
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Complicating Factor
Transmission of signal can be disrupted by noise
Noise could be caused by the medium/channel used
Noise source: generates noise
Increase the signal, increase the noise
If signal is amplified, noise is amplified too
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Amplifying Signal
Source: Douglas, C (2016) Computer Networks and Internets
Signal to noise ratio will remain constant
P1 : N1 = P2 : N2
Noise level N1
Noise level N2
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Communication Model
Source: https:// www.youtube.com / watch?v =OY1JsGFZprc
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Practice 7.1
Describe the SIX components in the Shannon’s communication model.
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Lesson 7 Outline
Data Communications
Communication Model
Physics of Transmission
Types of Signal
Representing Signals
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Physics of Transmission
Most functions on physical layer depends on characteristics of physical medium
Each physical medium requires own physical layer
Before looking into the functions, we need to consider some basic physics
like electromagnetism including electric conduction and electromagnetic radiation
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Transmitting Information
Data communications deals with two types of signals to transmit information:
analog
digital
Analog signal is characterized by continuous signal levels
When input changes from one value to next, it does so by moving through all possible intermediate values
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Analog vs Digital Signal
A digital signal has a fixed set of valid levels
Each change consists of an instantaneous move from one valid level to another
Source: Douglas, C (2016) Computer Networks and Internets
Analog
Digital
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Signal Classification
Signals are broadly classified as
periodic - repeated
aperiodic - sometimes called nonperiodic
Classification depends on whether they repeat
Left: aperiodic as the signal does not repeat
Right: periodic as the signal repeats
Source: Douglas, C (2016) Computer Networks and Internets
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Sine Waves
Much analysis in data communications involves the use of sinusoidal trigonometric functions
Especially sine, abbreviated sin
Sine wave: periodic wave that oscillates regularly and smoothly between negative and positive value
Source: Bing, licensed under CC BY-SA
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Sine Waves: Superimposed
Two sine waves are superimposed exactly on each other
If they are in the same phase
Two sine waves cannot superimpose on each other
If one of the waves of the same frequency has crest slightly later than the other
They are said to be out of phase
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Sine Waves Importance
Sine waves are especially important in information sources
Natural phenomena produce sine waves
A microphone picks up an audible tone, the output is a sine
Electromagnetic radiation can be represented as sine wave
We are interested in sine waves that correspond to a signal that oscillates in time
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Sine Waves Shape
Importance of sine waves is not just that signals often carried by them
Like in fibre optics, wireless transmission and communications using modems
The shapes are also important
Square shaped digital signal can be represented by a series of sine waves of different frequencies
Help engineers to analyse and design transmission systems
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Signal Characteristics
Frequency: the number of oscillations per unit time (usually seconds)
Amplitude: the difference between the maximum and minimum signal heights
Phase: how far the start of the sine wave is shifted from a reference time
Wavelength: length of a cycle as a signal propagates across a medium
Determined by speed which signal propagates
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Speed of Waves
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Electromagnetic Spectrum
Source: Douglas, C (2016) Computer Networks and Internets
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Visualising Signal Characteristics
Signal characteristics can be expressed mathematically
Source: Douglas, C (2016) Computer Networks and Internets
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Signal Observations (1/3)
Frequency can be calculated as inverse of the time required for one cycle, which is known as period
The example (a) has:
Period T = 1 seconds
Frequency of 1 / T or 1 Hertz
The example (b) has
Period T = 0.5 seconds
Frequency of 2 Hertz
Source: Douglas, C (2016) Computer Networks and Internets
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Signal Observation (2/3)
Both (a) and (b) are extremely low frequencies
Typical communication systems use high frequencies measured in millions of cycles per second
Source: Douglas, C (2016) Computer Networks and Internets
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Signal Observation (3/3)
To clarify high frequencies, engineers express time in fractions of a second
OR express frequency in units like megahertz (MHz)
There are other orders of time to express frequency
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Time & Frequency Units
Source: Douglas, C (2016) Computer Networks and Internets
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Practice 7.2
Describe the FOUR signal characteristics.
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Lesson 7 Outline
Data Communications
Types of Signal
Representing Signals
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Simple Signals
Signals like the ones illustrated below are classified as simple
They consist of a sine wave that cannot be decomposed further
Source: Douglas, C (2016) Computer Networks and Internets
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Composite Signals
However, most signals are classified as composite
signal can be decomposed into a set of simple sine waves
Source: Douglas, C (2016) Computer Networks and Internets
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Importance of Composite Signal
Data communications concepts mostly relates to sine functions and composite signals
In modulation and demodulation, one of the primary reasons:
Signals that result from modulation are usually composite signals
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Fourier Analysis (1/2)
A mathematician named Fourier discovered that
Possible to decompose a composite signal into its constituent parts
Each part is a sine function with frequency amplitude and phase
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Fourier Analysis (2/2)
Analysis by Fourier shows that if composite signal is periodic, the constituent parts will also be periodic
Most systems use composite signals to carry information
Composite signal is created at the sending end
Receiver decomposes the signal into simple components
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Fourier Analysis Result
Harmonics: frequencies from multiples of a base frequency
Mathematics behind this is known as Fourier Analysis
Signal of any shape can be represented by series of sine waves of different harmonic frequencies
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Lesson 7 Outline
Data Communications
Types of Signal
Representing Signals
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Representing Composite Signals
Several methods have been invented to represent composite signals
Time domain: graph of signal as function of time
Frequency domain: graph of frequency vs amplitude
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Frequency Domain
Frequency domain graph shows a set of simple sine waves that constitute a composite function
y-axis gives the amplitude
x-axis gives the frequency
Source: Douglas, C (2016) Computer Networks and Internets
Frequency domain of
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Frequency Domain Benefits
Frequency domain representation can also be used with nonperiodic signals
Compactness: frequency domain graph is small and easy to read as each sine wave occupies a single point along the x-axis
Good when a composite signal contains many simple signals
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Bandwidth
Range of frequencies that can be effectively carried by the channel
Measures the difference between the upper and lower level frequency of transmission
In other words, it measures the number of times a signal oscillates per second
Unit of measurement: Hertz (Hz)
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Maximum Bit Rate Achievable
Dependent on ability of receiver to discern level of signals received without errors
Depends on the effects of transmission impairments, particularly noise
There are two useful theorem:
Nyquist’s theorem
Shannon’s law
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Nyquist Theorem
Nyquist Theorem: considers a noiseless channel when calculating maximum theoretical capacity of a channel
Nyquist Theorem: C = 2B log2V
V is the number of signaling levels used to carry the signals
C is the maximum theoretical capacity in bit/s
B is the bandwidth in Hertz (Hz)
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Nyquist Theorem Example
Suppose a 3.1 kHz telephone circuit in which signal is carried using 32 signaling levels
Using Nyquist Theorem:
C = 2B log2V
= 2 x 3100 x log232
= 6200 x 5
= 31,000 bit/s
= 31 kbit/s
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Practice 7.3
A signal making use of 64 separate signaling states is transmitted in a channel between the frequencies of 2kHz and 2.4 kHz.
What is the maximum achievable data rate in this channel?
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Shannon’s Law
Shannon’s Law: considers a noisy channel by using signal to noise ratio when calculating maximum theoretical capacity of a channel
Shannon’s Law: C = B log2 (1 + S/N)
C is the maximum theoretical capacity in bit/s
B is the bandwidth in Hertz (Hz)
S is the signal power in Watts (W)
N is the noise power in Watts (W)
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Signal to Noise Ratio
Signal to Noise Ratio (SNR) is calculated using
SNR = 10 log10 (S/N)
S is the power of signal
N is the power of noise
Unit of measurement: deciBel (dB)
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Shannon’s Law Example (1/2)
Suppose a 3.1 kHz telephone circuit with a signal to noise ratio of 40dB
Converting 40dB to real ratio:
40 = 10 log10 S/N
4 = log10 S/N
104 = S/N
S/N = 10,000
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Shannon’s Law Example (2/2)
Using Shannon’s law to calculate the theoretical maximum capacity
C = B log2(1 + S/N)
= 3,100 log2 (1 + 10000)
= 3,100 log2 (10,001)
= 3,100 x 13.2879
= 41,192 bit/s
= 41.2 kbit/s
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Practice 7.4
A microwave radio signal is broadcast between the frequencies of 1 GHz and 1.1 GHz between two radio towers where it is affected by noise of power 2mW.
If the signal must carry 1 Gbit/s of data, calculate minimum level of power that will be required in the transmitter.
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Extreme Cases to Consider
If signal do not change at all over time, frequency range of the component sine waves is 0
Requires no bandwidth
If the signal change abruptly from one level to another, like a square wave, frequency range of the component sine waves is infinite
Requires infinite bandwidth
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Infinite Range of Frequencies
No medium can support infinite range of frequencies
All media must remove higher frequency components from the signal
No medium can perfectly carry a square shaped wave
Shape will be distorted when higher frequency components are removed
Shape of the signal received will not have perfectly straight edges
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Reading
Douglas, C. (2016). Computer Networks and Internets, Global Edition (6th ed.). Pearson Education. ISBN: 978-1292061177 Chapter 6
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End of Lesson
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