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Communications Systems
Course InformationCourse Information
• Lecturer: Dr. Muhammad Saleem Awan
– Email: awan01407@hotmail.com
• Handouts
– Slides: exam is based on slides
– Presentations from students
– Problem sheets
• Grading
– 6 quizzes (10%), 3 Assignments (10%), Mid term (20%), End term (60%)
•You’re welcome to ask questions
– You can interrupt me at any time.
– Please don’t disturb others in the class
•Our responsibility is to facilitate you to learn. You have to make the effort.
• Spend time reviewing lecture notes afterwards
– It isn’t to watch a movie!
• If you have a question on the lecture material after a class, then
– Look up a book! Be resourceful.
– Try to work it out yourself.
– Ask me during the problem class or one of scheduled times of availability
Course OutlinesCourse Outlines
• Week 1 – Introduction to communication systems & media bandwidth
•Week 2 – Transmission impairments, channel capacity
• Week 3 – Study of twisted pair & its transmission characteristics
• Week 4 – Study of coaxial cable & its transmission characteristics
• Week 5 – Introduction to optical fiber communication systems
• Week 6 – Introduction to wireless medium, Antenna basics, polarization
• Week 7 – Terrestrial microwave transmission characteristics
• Week 8 – Introduction to satellite communication system
• Week 9 – Satellite Communication
• Week 10 – Circuit & packet switching
• Week 11 – Multiplexing, types, study of FDM
• Week 12 – Study of TDM
• Week 13 – Spread Spectrum Communication System (FHSS, DSSS)
• Week 14 – Introduction to CDMA & OFDM
• Week 15 – Introduction to Mobile & cellular communications
• Week 16 – Mobile & cellular communications
IndexIndex
•Introduction
• Communication?
• Evolution of communication?
• Electromagnetic Spectrum
• Historical Background?
•Communication System
• Electrical Communication System
• Analog Communication System
• Digital Communication System
•Classification of Communication Systems
• Topology?
• Point-to-Point or Broadcast?
• Underwater, Terrestrial, ground-space or space to space links?
• Channel Distances?
• Wired or Wireless?
•Important Communication Systems
• Radio Communication Systems?
• Optical Communication Systems?
• Satellite Communication Systems?
• Terrestrial Microwave Communication System?
• Summary
Communication is the transfer of information from one place to
another.
This should be done
- as efficiently as possible
- with as much fidelity/reliability as possible
- as securely as possible
Communication System: Components/subsystems act together to
accomplish information transfer/exchange.
OverviewOverview
Input Transducer: The message produced by a source must be converted by a
transducer to a form suitable for the particular type of communication system.
Example: In electrical communications, speech waves are converted by a
microphone to voltage variation.
Transmitter: The transmitter processes the input signal to produce a signal suits
to the characteristics of the transmission channel.
Signal processing for transmission almost always involves modulation and may
also include coding. In addition to modulation, other functions performed by the
transmitter are amplification, filtering and coupling the modulated signal to the
channel.
Remember the components of a communications system:
Channel: The channel can have different forms: The atmosphere (or free
space), coaxial cable, fiber optic, waveguide, etc.
The signal undergoes some amount of degradation from noise, interference
and distortion
Receiver: The receiver’s function is to extract the desired signal from the
received signal at the channel output and to convert it to a form suitable for
the output transducer.
Other functions performed by the receiver: amplification (the received signal
may be extremely weak), demodulation and filtering.
Output Transducer: Converts the electric signal at its input into the form
desired by the system user.
Example: Loudspeaker, personal computer (PC), tape recorders.
Remember the components of a communications system:
Communication Systems
What goes into the
engineering of these
systems?
Key Ingredients
• Software
• Hardware
• Communication architecture, with coding
and signal processing algorithms
• How do you communicate?
• The history of communication goes back
thousands of years.
• What has this progress meant to you
today?
The Evolution of Communication
• Verbal Communication
• The most common form of communication.
– Spoken communication
– Languages and dialects
• What dialects are spoken in your area?
– In the country?
The Evolution of Communication
• Written Communication
– Symbols, hieroglyphics, and drawings
– The Chinese invent paper
The Evolution of Communication
Communication has a
long history
• Smoke signals, telegraph,
telephone…
• 1895: invention of the
radio by Marconi
• 1901: trans-atlantic
communication
State of affairs:
Early 20th
century
• Most communication systems are analog.
• Engineering designs are ad-hoc, tailored for
each specific application.
50 years later….
• Our communication infrastructure is going
fully digital.
• Most modern communication systems are
designed according to the principles laid
down by Shannon.
Internet
S
D
Lessons for Us
• Think different
• Think big
• Think simple
To be transmitted, Information (Data)
must be transformed to electromagnetic
signals.
Electromagnetic WavesElectromagnetic Waves
..
Electromagnetic WavesElectromagnetic Waves
..
Electromagnetic Spectrum
http://www.edumedia-sciences.com/a185_l2-transverse-
electromagnetic-wave.html
Electromagnetic Spectrum
Wave length Frequency
Designations
Transmission
Media
Propagation
Modes
Representative
Applications
Frequency
1 cm
Extra High
Frequency (EHF) 100 GHz
10 cm
Super High
Frequency (SHF)
Satellite,
Microwave relay,
Earth-satellite radar.
10 GHz
1 m
Ultra High
Frequency (UHF)
Wireless comm.
service,
Cellular, pagers, UHF
TV
1 GHz
10m
Very High
Frequency (VHF)
Mobile, Aeronautical,
VHF TV and FM,
mobile radio 100 MHz
100m
High Frequency
(HF)
Amateur radio, Civil
Defense 10 MHz
1 km
Medium High
Frequency (MF)
AM broadcasting
1 MHz
10 km
Low Frequency
(LF) 100 kHz
100km
Very Low
Frequency (VLF)
Wave guide
Coaxial Cable
Wire pairs
Line-of-sight radio
Sky wave radio
Ground wave
radio
Aeronautical,
Submarine cable,
Navigation,
Transoceanic radio
10 kHz
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There are many kinds of information sources, which can be
categorized into two distinct message categories, analog and
digital.
an analog communication system should deliver this waveform
with a specified degree of fidelity.
a digital communication system should deliver data with a
specified degree of accuracy in a specified amount of time.
Analog and Digital Communication Systems
Basic analog communications system
Modulator
Demodulator
Transmission
Channel
Input
transducer
Transmitter
Receiver
Output
transducer
Carrier
EM waves (modulated signal)
EM waves (modulated
signal)
Baseband signal
(electrical signal)
Baseband signal
(electrical signal)
Communication systems v1
Types of Analog Modulation
 Amplitude Modulation (AM)
 Amplitude modulation is the process of varying the amplitude of a
carrier wave in proportion to the amplitude of a baseband signal. The
frequency of the carrier remains constant
 Frequency Modulation (FM)
 Frequency modulation is the process of varying the frequency of a
carrier wave in proportion to the amplitude of a baseband signal. The
amplitude of the carrier remains constant
 Phase Modulation (PM)
 Another form of analog modulation technique which we will not discuss
Amplitude Modulation
Carrier wave
Baseband signal
Modulated wave
Amplitude varying-
frequency constant
Frequency Modulation
Carrier wave
Baseband signal
Modulated wave
Frequency varying-
amplitude constant
Large amplitude:
high frequency
Small amplitude:
low frequency
AM vs. FM
• AM requires a simple circuit, and is very easy to generate.
• It is simple to tune, and is used in almost all short wave broadcasting.
• The area of coverage of AM is greater than FM (longer wavelengths (lower frequencies)
are utilized-remember property of HF waves?)
• However, it is quite inefficient, and is susceptible to static and other forms of electrical
noise.
• The main advantage of FM is its audio quality and immunity to noise. Most forms of
static and electrical noise are naturally AM, and an FM receiver will not respond to AM
signals.
• The audio quality of a FM signal increases as the frequency deviation increases
(deviation from the center frequency), which is why FM broadcast stations use such
large deviation.
• The main disadvantage of FM is the larger bandwidth it requires
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Information Representation
• Communication system converts information into electrical
electromagnetic/optical signals appropriate for the transmission
medium.
• Analog systems convert analog message into signals that can propagate
through the channel.
• Digital systems convert bits (digits, symbols) into signals
– Computers naturally generate information as characters/bits
– Most information can be converted into bits
– Analog signals converted to bits by sampling and quantizing (A/D
conversion)
Goals in Communication System Design
• To maximize transmission rate, R
• To maximize system utilization, U
• To minimize bit error rate, Pe
• To minimize required systems bandwidth, W
• To minimize system complexity, Cx
• To minimize required power, Eb/No
Signal Nomenclature
• Information Source
– Discrete output values e.g. Keyboard
– Analog signal source e.g. output of a microphone
• Character
– Member of an alphanumeric/symbol (A to Z, 0 to 9)
– Characters can be mapped into a sequence of binary digits using
one of the standardized codes such as
• ASCII: American Standard Code for Information Interchange
• EBCDIC: Extended Binary Coded Decimal Interchange Code
Signal Nomenclature
• Digital Message
– Messages constructed from a finite number of symbols; e.g., printed
language consists of 26 letters, 10 numbers, “space” and several
punctuation marks. Hence a text is a digital message constructed from
about 50 symbols
– Morse-coded telegraph message is a digital message constructed from
two symbols “Mark” and “Space”
• M - ary
– A digital message constructed with M symbols
• Digital Waveform
– Current or voltage waveform that represents a digital symbol
• Bit Rate
– Actual rate at which information is transmitted per second
Signal Nomenclature
• Baud Rate
– Refers to the rate at which the signaling elements are
transmitted, i.e. number of signaling elements per
second.
• Bit Error Rate
– The probability that one of the bits is in error or simply
the probability of error
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1 Ground Wave Propagation
Follows contour of the earth Can Propagate considerable distances
Frequencies up to 2 MHz Example : AM radio
Radio Wave Communication Systems
2 Sky Wave Propagation
Signal reflected from ionized layer
of atmosphere. Signal can travel
a number of hops, back and forth
Examples SW radio
3 Line-of-Sight Propagation
Transmitting and receiving antennas
must be within line of sight
example
Satellite communication
Ground communication
Figure Comparison of analog and digital signals
Signals can be analog or digital.
Analog signals can have an infinite number of values in a range; digital
signals can have only a limited
number of values.
PERIODIC ANALOG SIGNALSPERIODIC ANALOG SIGNALS
Periodic analog signals can be classified as simple or composite. A
simple periodic analog signal, a sine wave, cannot be decomposed
into simpler signals. A composite
periodic analog signal is composed of multiple sine waves.
Sine Wave
Wavelength
Time and Frequency Domain
Composite Signals
Bandwidth
Topics discussed in this section:Topics discussed in this section:
In communication systems, we commonly use periodic
analog signals and nonperiodic digital signals.
Figure A sine wave
Figure Two signals with the same phase and frequency,
but different amplitudes
Frequency and period are the inverse of each other.
• Frequency is the rate of change with respect to time.
• Change in a short span of time means high frequency.
• Change over a long span of time means low frequency.
If a signal does not change at all, its frequency is zero.
If a signal changes instantaneously, its frequency is infinite.
Figure Two signals with the same amplitude and phase,
but different frequencies
Table Units of period and frequency
The period of a signal is 100 ms. What is its frequency in kilohertz?
Example
Solution
First we change 100 ms to seconds, and then we calculate the
frequency from the period (1 Hz = 10−3
kHz).
Figure Three sine waves with the same amplitude and frequency,
but different phases
Phase describes the position of the waveform relative to time 0.
A sine wave is offset 1/6 cycle with respect to time 0. What is its phase in
degrees and radians?
Example
Solution
We know that 1 complete cycle is 360°. Therefore, 1/6 cycle is
Figure Wavelength and period
Figure The time-domain and frequency-domain plots of a sine wave
Time and frequency domains
Time and frequency domains (continued)
A complete sine wave in the time domain can be represented by one single
spike in the frequency domain.
The frequency domain is more compact and useful when we are
dealing with more than one sine wave. For example, Next Figure
shows three sine waves, each with different amplitude and
frequency. All can be represented by three spikes in the frequency
domain.
Example
Figure The time domain and frequency domain of three sine waves
Example Amplitude modulation
Figure AM band allocation
Each AM radio station is assigned a 10-kHz bandwidth. The total bandwidth
dedicated to AM radio ranges from 530 to 1700 kHz.
Example
Figure Frequency modulation
Figure FM band allocation
Each FM radio station is assigned a 200-kHz bandwidth. The total bandwidth
dedicated to FM radio ranges from 88 to 108 MHz.
Example
According to Fourier analysis, any
composite signal is a combination of
simple sine waves with different
frequencies, amplitudes, and phases.
A single-frequency sine wave is not useful in communication systems;
we need to send a composite signal, a signal made of many simple sine
waves.
If the composite signal is periodic, the
decomposition gives a series of signals
with discrete frequencies;
if the composite signal is nonperiodic,
the decomposition gives a combination
of sine waves with continuous
frequencies.
Figure A composite periodic signal
Above Figure shows a periodic composite signal with frequency f. This type of
signal is not typical of those found in data communications. We can consider it
to be three alarm systems, each with a different frequency. The analysis of
this signal can give us a good understanding of how to decompose signals.
Figure Decomposition of a composite periodic signal in the time and
frequency domains
Three harmonics
Square wave
Adding first three harmonics
Frequency spectrum comparison
A digital signal
A digital signal is a composite signal with an infinite bandwidth.
Figure The time and frequency domains of a nonperiodic signal
Above Figure shows a non-periodic composite signal. It can be the signal
created by a microphone or a telephone set when a word or two is pronounced.
In this case, the composite signal cannot be periodic, because that implies that
we are repeating the same word or words with exactly the same tone.
The bandwidth of a composite signal is
the difference between the
highest and the lowest frequencies
contained in that signal.
Figure The bandwidth of periodic and nonperiodic composite signals
If a periodic signal is decomposed into five sine waves with
frequencies of 100, 300, 500, 700, and 900 Hz, what is its
bandwidth? Draw the spectrum, assuming all components have a
maximum amplitude of 10 V.
Solution
Let fh be the highest frequency, fl the lowest frequency, and B the
bandwidth. Then
Example
The spectrum has only five spikes, at 100, 300, 500, 700, and 900
Hz (see next Figure).
Figure The bandwidth for Example
A periodic signal has a bandwidth of 20 Hz. The highest frequency is 60 Hz. What
is the lowest frequency? Draw the spectrum if the signal contains all frequencies
of the same amplitude.
Solution
Let fh be the highest frequency, fl the lowest frequency, and B the bandwidth.
Then
Example
The spectrum contains all integer frequencies. We show this by a series of
spikes (see next Figure).
Figure The bandwidth for Example
A nonperiodic composite signal has a bandwidth of 200 kHz, with a
middle frequency of 140 kHz and peak amplitude of 20 V. The two
extreme frequencies have an amplitude of 0. Draw the frequency
domain of the signal.
Example
Solution
The lowest frequency must be at 40 kHz
and the highest at 240 kHz. Next Figure
shows the frequency domain and the
bandwidth.
Figure The bandwidth for Example
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Analog signals of bandwidth W can be represented by 2W samples/s
Channels of bandwidth W support transmission of 2W symbols/s

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Communication systems v1

  • 2. Course InformationCourse Information • Lecturer: Dr. Muhammad Saleem Awan – Email: awan01407@hotmail.com • Handouts – Slides: exam is based on slides – Presentations from students – Problem sheets • Grading – 6 quizzes (10%), 3 Assignments (10%), Mid term (20%), End term (60%) •You’re welcome to ask questions – You can interrupt me at any time. – Please don’t disturb others in the class •Our responsibility is to facilitate you to learn. You have to make the effort. • Spend time reviewing lecture notes afterwards – It isn’t to watch a movie! • If you have a question on the lecture material after a class, then – Look up a book! Be resourceful. – Try to work it out yourself. – Ask me during the problem class or one of scheduled times of availability
  • 3. Course OutlinesCourse Outlines • Week 1 – Introduction to communication systems & media bandwidth •Week 2 – Transmission impairments, channel capacity • Week 3 – Study of twisted pair & its transmission characteristics • Week 4 – Study of coaxial cable & its transmission characteristics • Week 5 – Introduction to optical fiber communication systems • Week 6 – Introduction to wireless medium, Antenna basics, polarization • Week 7 – Terrestrial microwave transmission characteristics • Week 8 – Introduction to satellite communication system • Week 9 – Satellite Communication • Week 10 – Circuit & packet switching • Week 11 – Multiplexing, types, study of FDM • Week 12 – Study of TDM • Week 13 – Spread Spectrum Communication System (FHSS, DSSS) • Week 14 – Introduction to CDMA & OFDM • Week 15 – Introduction to Mobile & cellular communications • Week 16 – Mobile & cellular communications
  • 4. IndexIndex •Introduction • Communication? • Evolution of communication? • Electromagnetic Spectrum • Historical Background? •Communication System • Electrical Communication System • Analog Communication System • Digital Communication System •Classification of Communication Systems • Topology? • Point-to-Point or Broadcast? • Underwater, Terrestrial, ground-space or space to space links? • Channel Distances? • Wired or Wireless? •Important Communication Systems • Radio Communication Systems? • Optical Communication Systems? • Satellite Communication Systems? • Terrestrial Microwave Communication System? • Summary
  • 5. Communication is the transfer of information from one place to another. This should be done - as efficiently as possible - with as much fidelity/reliability as possible - as securely as possible Communication System: Components/subsystems act together to accomplish information transfer/exchange. OverviewOverview
  • 6. Input Transducer: The message produced by a source must be converted by a transducer to a form suitable for the particular type of communication system. Example: In electrical communications, speech waves are converted by a microphone to voltage variation. Transmitter: The transmitter processes the input signal to produce a signal suits to the characteristics of the transmission channel. Signal processing for transmission almost always involves modulation and may also include coding. In addition to modulation, other functions performed by the transmitter are amplification, filtering and coupling the modulated signal to the channel. Remember the components of a communications system:
  • 7. Channel: The channel can have different forms: The atmosphere (or free space), coaxial cable, fiber optic, waveguide, etc. The signal undergoes some amount of degradation from noise, interference and distortion Receiver: The receiver’s function is to extract the desired signal from the received signal at the channel output and to convert it to a form suitable for the output transducer. Other functions performed by the receiver: amplification (the received signal may be extremely weak), demodulation and filtering. Output Transducer: Converts the electric signal at its input into the form desired by the system user. Example: Loudspeaker, personal computer (PC), tape recorders. Remember the components of a communications system:
  • 8. Communication Systems What goes into the engineering of these systems?
  • 9. Key Ingredients • Software • Hardware • Communication architecture, with coding and signal processing algorithms
  • 10. • How do you communicate? • The history of communication goes back thousands of years. • What has this progress meant to you today? The Evolution of Communication
  • 11. • Verbal Communication • The most common form of communication. – Spoken communication – Languages and dialects • What dialects are spoken in your area? – In the country? The Evolution of Communication
  • 12. • Written Communication – Symbols, hieroglyphics, and drawings – The Chinese invent paper The Evolution of Communication
  • 13. Communication has a long history • Smoke signals, telegraph, telephone… • 1895: invention of the radio by Marconi • 1901: trans-atlantic communication
  • 14. State of affairs: Early 20th century • Most communication systems are analog. • Engineering designs are ad-hoc, tailored for each specific application.
  • 15. 50 years later…. • Our communication infrastructure is going fully digital. • Most modern communication systems are designed according to the principles laid down by Shannon. Internet S D
  • 16. Lessons for Us • Think different • Think big • Think simple
  • 17. To be transmitted, Information (Data) must be transformed to electromagnetic signals.
  • 22. Wave length Frequency Designations Transmission Media Propagation Modes Representative Applications Frequency 1 cm Extra High Frequency (EHF) 100 GHz 10 cm Super High Frequency (SHF) Satellite, Microwave relay, Earth-satellite radar. 10 GHz 1 m Ultra High Frequency (UHF) Wireless comm. service, Cellular, pagers, UHF TV 1 GHz 10m Very High Frequency (VHF) Mobile, Aeronautical, VHF TV and FM, mobile radio 100 MHz 100m High Frequency (HF) Amateur radio, Civil Defense 10 MHz 1 km Medium High Frequency (MF) AM broadcasting 1 MHz 10 km Low Frequency (LF) 100 kHz 100km Very Low Frequency (VLF) Wave guide Coaxial Cable Wire pairs Line-of-sight radio Sky wave radio Ground wave radio Aeronautical, Submarine cable, Navigation, Transoceanic radio 10 kHz
  • 46. There are many kinds of information sources, which can be categorized into two distinct message categories, analog and digital. an analog communication system should deliver this waveform with a specified degree of fidelity. a digital communication system should deliver data with a specified degree of accuracy in a specified amount of time. Analog and Digital Communication Systems
  • 47. Basic analog communications system Modulator Demodulator Transmission Channel Input transducer Transmitter Receiver Output transducer Carrier EM waves (modulated signal) EM waves (modulated signal) Baseband signal (electrical signal) Baseband signal (electrical signal)
  • 49. Types of Analog Modulation  Amplitude Modulation (AM)  Amplitude modulation is the process of varying the amplitude of a carrier wave in proportion to the amplitude of a baseband signal. The frequency of the carrier remains constant  Frequency Modulation (FM)  Frequency modulation is the process of varying the frequency of a carrier wave in proportion to the amplitude of a baseband signal. The amplitude of the carrier remains constant  Phase Modulation (PM)  Another form of analog modulation technique which we will not discuss
  • 50. Amplitude Modulation Carrier wave Baseband signal Modulated wave Amplitude varying- frequency constant
  • 51. Frequency Modulation Carrier wave Baseband signal Modulated wave Frequency varying- amplitude constant Large amplitude: high frequency Small amplitude: low frequency
  • 52. AM vs. FM • AM requires a simple circuit, and is very easy to generate. • It is simple to tune, and is used in almost all short wave broadcasting. • The area of coverage of AM is greater than FM (longer wavelengths (lower frequencies) are utilized-remember property of HF waves?) • However, it is quite inefficient, and is susceptible to static and other forms of electrical noise. • The main advantage of FM is its audio quality and immunity to noise. Most forms of static and electrical noise are naturally AM, and an FM receiver will not respond to AM signals. • The audio quality of a FM signal increases as the frequency deviation increases (deviation from the center frequency), which is why FM broadcast stations use such large deviation. • The main disadvantage of FM is the larger bandwidth it requires
  • 62. Information Representation • Communication system converts information into electrical electromagnetic/optical signals appropriate for the transmission medium. • Analog systems convert analog message into signals that can propagate through the channel. • Digital systems convert bits (digits, symbols) into signals – Computers naturally generate information as characters/bits – Most information can be converted into bits – Analog signals converted to bits by sampling and quantizing (A/D conversion)
  • 63. Goals in Communication System Design • To maximize transmission rate, R • To maximize system utilization, U • To minimize bit error rate, Pe • To minimize required systems bandwidth, W • To minimize system complexity, Cx • To minimize required power, Eb/No
  • 64. Signal Nomenclature • Information Source – Discrete output values e.g. Keyboard – Analog signal source e.g. output of a microphone • Character – Member of an alphanumeric/symbol (A to Z, 0 to 9) – Characters can be mapped into a sequence of binary digits using one of the standardized codes such as • ASCII: American Standard Code for Information Interchange • EBCDIC: Extended Binary Coded Decimal Interchange Code
  • 65. Signal Nomenclature • Digital Message – Messages constructed from a finite number of symbols; e.g., printed language consists of 26 letters, 10 numbers, “space” and several punctuation marks. Hence a text is a digital message constructed from about 50 symbols – Morse-coded telegraph message is a digital message constructed from two symbols “Mark” and “Space” • M - ary – A digital message constructed with M symbols • Digital Waveform – Current or voltage waveform that represents a digital symbol • Bit Rate – Actual rate at which information is transmitted per second
  • 66. Signal Nomenclature • Baud Rate – Refers to the rate at which the signaling elements are transmitted, i.e. number of signaling elements per second. • Bit Error Rate – The probability that one of the bits is in error or simply the probability of error
  • 70. 1 Ground Wave Propagation Follows contour of the earth Can Propagate considerable distances Frequencies up to 2 MHz Example : AM radio Radio Wave Communication Systems
  • 71. 2 Sky Wave Propagation Signal reflected from ionized layer of atmosphere. Signal can travel a number of hops, back and forth Examples SW radio 3 Line-of-Sight Propagation Transmitting and receiving antennas must be within line of sight example Satellite communication Ground communication
  • 72. Figure Comparison of analog and digital signals Signals can be analog or digital. Analog signals can have an infinite number of values in a range; digital signals can have only a limited number of values.
  • 73. PERIODIC ANALOG SIGNALSPERIODIC ANALOG SIGNALS Periodic analog signals can be classified as simple or composite. A simple periodic analog signal, a sine wave, cannot be decomposed into simpler signals. A composite periodic analog signal is composed of multiple sine waves. Sine Wave Wavelength Time and Frequency Domain Composite Signals Bandwidth Topics discussed in this section:Topics discussed in this section: In communication systems, we commonly use periodic analog signals and nonperiodic digital signals.
  • 75. Figure Two signals with the same phase and frequency, but different amplitudes
  • 76. Frequency and period are the inverse of each other. • Frequency is the rate of change with respect to time. • Change in a short span of time means high frequency. • Change over a long span of time means low frequency. If a signal does not change at all, its frequency is zero. If a signal changes instantaneously, its frequency is infinite.
  • 77. Figure Two signals with the same amplitude and phase, but different frequencies
  • 78. Table Units of period and frequency
  • 79. The period of a signal is 100 ms. What is its frequency in kilohertz? Example Solution First we change 100 ms to seconds, and then we calculate the frequency from the period (1 Hz = 10−3 kHz).
  • 80. Figure Three sine waves with the same amplitude and frequency, but different phases Phase describes the position of the waveform relative to time 0.
  • 81. A sine wave is offset 1/6 cycle with respect to time 0. What is its phase in degrees and radians? Example Solution We know that 1 complete cycle is 360°. Therefore, 1/6 cycle is
  • 83. Figure The time-domain and frequency-domain plots of a sine wave
  • 85. Time and frequency domains (continued) A complete sine wave in the time domain can be represented by one single spike in the frequency domain.
  • 86. The frequency domain is more compact and useful when we are dealing with more than one sine wave. For example, Next Figure shows three sine waves, each with different amplitude and frequency. All can be represented by three spikes in the frequency domain. Example
  • 87. Figure The time domain and frequency domain of three sine waves
  • 89. Figure AM band allocation Each AM radio station is assigned a 10-kHz bandwidth. The total bandwidth dedicated to AM radio ranges from 530 to 1700 kHz. Example
  • 91. Figure FM band allocation Each FM radio station is assigned a 200-kHz bandwidth. The total bandwidth dedicated to FM radio ranges from 88 to 108 MHz. Example
  • 92. According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases. A single-frequency sine wave is not useful in communication systems; we need to send a composite signal, a signal made of many simple sine waves.
  • 93. If the composite signal is periodic, the decomposition gives a series of signals with discrete frequencies; if the composite signal is nonperiodic, the decomposition gives a combination of sine waves with continuous frequencies.
  • 94. Figure A composite periodic signal Above Figure shows a periodic composite signal with frequency f. This type of signal is not typical of those found in data communications. We can consider it to be three alarm systems, each with a different frequency. The analysis of this signal can give us a good understanding of how to decompose signals.
  • 95. Figure Decomposition of a composite periodic signal in the time and frequency domains
  • 97. Adding first three harmonics
  • 99. A digital signal A digital signal is a composite signal with an infinite bandwidth.
  • 100. Figure The time and frequency domains of a nonperiodic signal Above Figure shows a non-periodic composite signal. It can be the signal created by a microphone or a telephone set when a word or two is pronounced. In this case, the composite signal cannot be periodic, because that implies that we are repeating the same word or words with exactly the same tone.
  • 101. The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal.
  • 102. Figure The bandwidth of periodic and nonperiodic composite signals
  • 103. If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is its bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V. Solution Let fh be the highest frequency, fl the lowest frequency, and B the bandwidth. Then Example The spectrum has only five spikes, at 100, 300, 500, 700, and 900 Hz (see next Figure).
  • 104. Figure The bandwidth for Example
  • 105. A periodic signal has a bandwidth of 20 Hz. The highest frequency is 60 Hz. What is the lowest frequency? Draw the spectrum if the signal contains all frequencies of the same amplitude. Solution Let fh be the highest frequency, fl the lowest frequency, and B the bandwidth. Then Example The spectrum contains all integer frequencies. We show this by a series of spikes (see next Figure).
  • 106. Figure The bandwidth for Example
  • 107. A nonperiodic composite signal has a bandwidth of 200 kHz, with a middle frequency of 140 kHz and peak amplitude of 20 V. The two extreme frequencies have an amplitude of 0. Draw the frequency domain of the signal. Example Solution The lowest frequency must be at 40 kHz and the highest at 240 kHz. Next Figure shows the frequency domain and the bandwidth.
  • 108. Figure The bandwidth for Example
  • 113. Analog signals of bandwidth W can be represented by 2W samples/s Channels of bandwidth W support transmission of 2W symbols/s