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Data and Computer Communications
Chapter 3Data Transmission
Required Reading: Stallings chapter 3
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Physical Layer
Application
Presentation
Session
transport
Network
Data link
Physical
Application
Presentation
Session
transport
Network
Data link
Physical
Network
Data link
Physical
Source node Destination node
Intermediate node
Signals
Packets
Bits
Frames
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Physical / Data Link Layer Interface
NL
DLL
PL
Frame
HDR
ACKHDR
Sender Receiver
Transmitted Bits
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Physical Layer Communications and Information Theory are
topics of whole courses We’ll cover some theoretical basics regarding
communications over a physical channel We discover that there are physical limitations
to communications over a given channel We’ll cover some fundamental theorems
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Terminology (1)TransmitterReceiverMedium
Guided mediume.g. twisted pair, optical fiber
Unguided mediume.g. air, water, vacuum
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Terminology (2)Direct link
No intermediate devicesPoint-to-point
Direct link Only 2 devices share link
Multi-point More than two devices share the link
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Terminology (3)Simplex
One direction (but in Europe means half duplex)
e.g. TelevisionHalf duplex
Either direction, but only one way at a timee.g. police radio
Full duplex Both directions at the same time
e.g. telephone
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Electromagnetic SignalsFunction of time
Analog (varies smoothly over time) Digital (constant level over time, followed by a
change to another level)Function of frequency
Spectrum (range of frequencies) Bandwidth (width of the spectrum)
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Frequency, Spectrum and BandwidthTime domain concepts
Continuous signalVaries in a smooth way over time
Discrete signalMaintains a constant level then changes to another
constant level Periodic signal
Pattern repeated over time Aperiodic signal
Pattern not repeated over time
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Periodic Signal Characteristics Amplitude (A): signal value, measured in volts Frequency (f ): repetition rate, cycles per
second or Hertz Period (T): amount of time it takes for one
repetition, T=1/f Phase (Φ): relative position in time, measured
in degrees or radians
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time(sec)am
plitu
de (v
olts
)
1 cycle
frequency (hertz)= cycles per second
phase difference
Analog Signalingrepresented by sine waves
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Digital Signalingrepresented by square waves or pulses
time(sec)am
plitu
de (v
olts
)
1 cycle
frequency (hertz)= cycles per second
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Continuous & Discrete Signals
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PeriodicSignals
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Sine WavePeak Amplitude (A)
maximum strength of signal volts
Frequency (f) Rate of change of signal Hertz (Hz) or cycles per second Period = time for one repetition (T) T = 1/f
Phase () Relative position in time
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Varying Sine Waves
Sin2πt 0.5Sin2πt
Sin4πt
2Sin
)4
2( tSinor
)125.0(2 tSin
Phase Shift in seconds
Phase Shift in radians
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Wavelength ()Distance occupied by one cycleDistance between two points of
corresponding phase in two consecutive cycles
Assuming signal velocity in space is equal to v = vT or f = v Here, V=c = 3*108 ms-1 (speed of light in free
space)
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Frequency Domain ConceptsA Signal is usually made up of many
frequenciesComponents are sine wavesIt Can be shown (Fourier analysis) that
any signal is made up of component sine waves
One can plot frequency domain functions instead of/in addition to time domain functions
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Addition of FrequencyComponents
(a) Sin(2πft)
(b) (1/3)Sin(2π(3f)t)
(c) (4/π)[Sin(2πft)+(1/3)Sin(2π(3f)t)]
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FrequencyDomain
Note: For square waves, only odd harmonics exist (plus the fundamental component of course).
(a) Frequency domain function for s(t)=(4/π)[Sin(2πft)+(1/3)Sin(2π(3f)t)]
(b) Frequency domain function for a single square pulse s(t)=1 for -X/2<t<X/2
Figure a is discrete because the time domain function is periodic. Figure b is continuous because the time domain function is aperiodic.
See Figure 3.16 Page 103. Note that s(f) is of the form
XSinX
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Communications Basics Represent a signal as a single-valued function of
time, g(t), to model behavior of a signal (may be voltage, current or other change)
Jean-Baptiste Fourier showed we can represent a periodic signal (given some conditions) as the sum of a possibly infinite number of sines and cosines
Period = Tg(t) = (1/2)c + an sin(2nft) + bn cos(2nft)
n=1 n=1f = 1/T is fundamental frequencya & b coefficients are the amplitude of the nth harmonic
This is a Fourier Series
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Time -> Harmonic spectrumOriginal
As we add more harmonics the signal reproduces the original more closely
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No transmission facility can transmit signals without losing some power
Usually this attenuation is frequency dependent so the signal becomes distorted
Generally signal is completely attenuated above some max frequency (due to medium characteristics or intentional filtering)
The signal is bandwidth limited
Signal Transmission
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Time T necessary to transmit a character depends on coding method and signalling speed
Signaling speed = number of times per second the signal changes value and is measured in baud
Note that baud rate is not necessarily the same as the bit rate
By limiting the bandwidth of the signal we also limit the data rate even if a channel is perfect
Overcome this by encoding schemes
Signal Transmission
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Spectrum & BandwidthSpectrum
range of frequencies contained in signalAbsolute bandwidth
width of spectrumEffective bandwidth
Often just bandwidth Narrow band of frequencies containing most of
the energyDC Component
Component of zero frequency
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Signal with DC Component
(a) s(t)=1+(4/π)[Sin(2πft)+(1/3)Sin(2π(3f)t)]
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Data Rate and BandwidthAny transmission system has a limited
band of frequenciesThis limits the data rate that can be
carriedSee Figure 3.8 Page 79
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BandwidthWidth of the spectrum of frequencies that
can be transmitted if spectrum=300 to 3400Hz,
bandwidth=3100HzGreater bandwidth leads to greater costsLimited bandwidth leads to distortionAnalog measured in Hertz, digital
measured in baud
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BPS vs. BaudBPS=bits per secondBaud=# of signal changes per secondEach signal change can represent more
than one bit, through variations on amplitude, frequency, and/or phase
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Analog and Digital Data TransmissionData
Entities that convey meaningSignals
Electric or electromagnetic representations of data
Transmission Communication of data by propagation and
processing of signals
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DataAnalog
Continuous values within some interval e.g. sound, video
Digital Discrete values e.g. text, integers
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Acoustic Spectrum (Analog)
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SignalsMeans by which data are propagatedAnalog
Continuously variable Various media
wire, fiber optic, space Speech bandwidth 100Hz to 7kHz Telephone bandwidth 300Hz to 3400Hz Video bandwidth 4MHz
Digital Use two DC components
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Digital Text SignalingTransmission of electronic pulses
representing the binary digits 1 and 0How do we represent letters, numbers,
characters in binary form?Earliest example: Morse code (dots and
dashes)Most common current form: ASCII
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ASCII Character CodesUse 8 bits of data (1 byte) to transmit one
character8 binary bits has 256 possible outcomes (0
to 255)Represents alphanumeric characters, as
well as “special” characters
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Digital Image Signaling Pixelization and binary representation
Code: 0000000000111100011101100111111001111000011111100011110000000000
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Data and SignalsUsually use digital signals for digital data
and analog signals for analog dataCan use analog signal to carry digital data
ModemCan use digital signal to carry analog data
Compact Disc audio
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Why Study Analog?Telephone system is primarily analog
rather than digital (designed to carry voice signals)
Low-cost, transmission medium (present almost at all places at all times
If we can convert digital information (1s and 0s) to analog form (audible tone), it can be transmitted inexpensively
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Voice SignalsEasily converted from sound frequencies
(measured in loudness/db) to electromagnetic frequencies, measured in voltage
Human voice has frequency components ranging from 20Hz to 20kHz
For practical purposes, the telephone system has a narrower bandwidth than human voice, from 300 to 3400Hz
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Analog Signals Carrying Analog and Digital Data
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Digital Signals Carrying Analog and Digital Data
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Analog TransmissionAnalog signal transmitted without regard
to contentMay be analog or digital dataAttenuated over distance Use amplifiers to boost signalAlso amplifies noise
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Digital TransmissionConcerned with contentIntegrity endangered by noise,
attenuation etc.Repeaters usedRepeater receives signalExtracts bit patternRetransmitsAttenuation is overcomeNoise is not amplified
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Advantages of Digital Transmission Digital technology
Low cost LSI/VLSI technology Data integrity
Longer distances over lower quality lines Capacity utilization
Economical high bandwidth links High degree of multiplexing easier with digital techniques
Security & Privacy Encryption
Integration Can treat analog and digital data similarly
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Transmission Mediathe physical path between transmitter and
receiverdesign factors
bandwidth attenuation: weakening of signal over
distances interference number of receivers
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Impairments and CapacityImpairments exist in all forms of data
transmissionAnalog signal impairments result in
random modifications that impair signal quality
Digital signal impairments result in bit errors (1s and 0s transposed)
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Transmission ImpairmentsSignal received may differ from signal
transmittedAnalog - degradation of signal qualityDigital - bit errorsCaused by
Attenuation and attenuation distortion Delay distortion Noise
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Transmission ImpairmentsAttenuation
loss of signal strength over distanceAttenuation Distortion
different losses at different frequenciesDelay Distortion
different speeds for different frequenciesNoise
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Attenuation
transmitter receiver
P1 watts P2 watts
Attenuation 10 log10 (P1/P2) dB
Amplification 10 log10 (P2/P1) dB
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AttenuationSignal strength falls off with distanceDepends on mediumReceived signal strength:
must be enough to be detected must be sufficiently higher than noise to be
received without errorAttenuation is an increasing function of
frequency
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Delay DistortionOnly in guided mediaPropagation velocity varies with frequency
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Noise (1)Additional signals inserted between
transmitter and receiverTypes of Noise:Thermal
Due to thermal excitement of electrons Uniformly distributed, cannot be eliminated White noise
Intermodulation Signals that are the sum and difference of
original frequencies sharing a medium
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Noise (2)Crosstalk
A signal from one line is picked up by another NEXT (near-end crosstalk )
interference in a wire at the transmitting end of a signal sent on a different wire
FEXT (far-end crosstalk) interference in a wire at the receiving end of a signal sent on a different wire
Impulse Irregular pulses or spikes e.g. External electromagnetic interference Short duration High amplitude Less predictable
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Noise
Effect distorts a transmitted signal attenuates a transmitted signal
signal-to-noise ratio to quantify noise
S/Ndb = 10 log S= average signal power
N= noise power
SN
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Effect of noise
Signal
Noise
Signal+Noise
0 1 1 1 1 0 0 0 0 1 Data Received
Sampling times
Bit error
0 1 0 1 1 0 0 1 0 1 Original data
Logic Threshold
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Channel CapacityData rate
In bits per second Rate at which data can be communicated
Bandwidth In cycles per second of Hertz Constrained by transmitter and medium
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Maximum Data Rate
In 1920s Nyquist (of the Nyquist Theorem) developed an equation for the maximum data rate of a noiseless channel For low pass filtered signal of bandwidth B Sampling at exactly 2B samples per sec allows
reconstruction of the signal More samples are useless since the
frequencies above B are filtered out
C=Capacity=max data rate = 2B log2 M bits/secfor M discrete levels
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Nyquist theorem
“ In a perfectly noiseless channel, if f is the maxmimum frequency the medium can transmit, the receiver can completely reconstruct a signal by sampling it 2*f times per second”
Nyquist, 1920
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Nyquist formula
M Max data rate (C) 2 6200 bps 4 12400 bps 8 18600 bps16 24800 bps
C = 2B log2 MB = bandwidthM = number of discrete signal levels
Theoretical capacity for Noiseless channel
Example: Channel capacity calculation for voice bandwidth (~3100 Hz):
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In the ‘40s Shannon (of Shannon’s Law) extended the equation to a channel subject to thermodynamic (thermal) noise Thermal noise measured by ratio of signal (S)
power to noise (N) power (signal-to-noise ratio - S/N)
But represented as: 10 log10 S/N These units are called decibels (dB) Now, for a channel with signal to noise of S/NCapacity=C=max bits/sec = B log2 (1 + S/N)
Shannon’s Law
Here, C=Theoretical Maximum capacity with noise
Note: Only much lower rates are achieved since the equation assumes zero impulse noise and no attenuation and delay distortion.
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Bit rate and Baud rate Bit rate number of bits that are transmitted in a second
Baud rate number of line signal changes (variations) per second
If a modem transmits 1 bit for every signal change
bit rate = baud rate
If a signal change represents 2 or more or n bits bit rate = baud rate *n