COE 342: Data

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COE 342 Data Computer Communications
(T042)Dr. Marwan Abu-Amara

• Chapter 3 Data Transmission

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Agenda

• Concepts Terminology
• Decibels and Signal Strength
• Fourier Analysis
• Analog Digital Data Transmission
• Transmission Impairments
• Channel Capacity

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Terminology (1)

• Transmitter
• Receiver
• Medium
• Guided medium
• e.g. twisted pair, optical fiber
• Unguided medium
• e.g. air, water, vacuum

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Terminology (2)

• Direct link
• No intermediate devices
• Point-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
• e.g. Television
• Half duplex
• Either direction, but only one way at a time
• e.g. police radio
• Full duplex
• Both directions at the same time
• e.g. telephone

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Frequency, Spectrum and Bandwidth

• Time domain concepts
• Analog signal
• Varies in a smooth way over time
• Digital signal
• Maintains 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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Analogue Digital Signals
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PeriodicSignals
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Sine Wave

• Peak 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 Wavess(t) A sin(2?ft ?)
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Wavelength

• Distance occupied by one cycle
• Distance between two points of corresponding
  phase in two consecutive cycles
• ?
• Assuming signal velocity v
• ? vT
• ?f v
• c 3108 m/sec (speed of light in free space)

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Frequency Domain Concepts

• Signal usually made up of many frequencies
• Components are sine waves
• Can be shown (Fourier analysis) that any signal
  is made up of component sine waves
• Can plot frequency domain functions

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Addition of FrequencyComponents(T1/f)
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FrequencyDomainRepresentations
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Spectrum Bandwidth

• Spectrum
• range of frequencies contained in signal
• Absolute bandwidth
• width of spectrum
• Effective bandwidth
• Often just bandwidth
• Narrow band of frequencies containing most of the
  energy
• DC Component
• Component of zero frequency

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Decibels and Signal Strength

• Decibel is a measure of ratio between two signal
  levels
• NdB number of decibels
• P1 input power level
• P2 output power level
• Example
• A signal with power level of 10mW inserted onto a
  transmission line
• Measured power some distance away is 5mW
• Loss expressed as NdB 10log(5/10)10(-0.3)-3 dB

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Decibels and Signal Strength

• Decibel is a measure of relative, not absolute,
  difference
• A loss from 1000 mW to 500 mW is a loss of 3dB
• A loss of 3 dB halves the power
• A gain of 3 dB doubles the power
• Example
• Input to transmission system at power level of 4
  mW
• First element is transmission line with a 12 dB
  loss
• Second element is amplifier with 35 dB gain
• Third element is transmission line with 10 dB
  loss
• Output power P2
• (-1235-10)13 dB 10 log (P2 / 4mW)
• P2 4 x 101.3 mW 79.8 mW

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Relationship Between Decibel Values and Powers of
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Power Ratio dB Power Ratio dB
101 10 10-1 -10
102 20 10-2 -20
103 30 10-3 -30
104 40 10-4 -40
105 50 10-5 -50
106 60 10-6 -60
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Decibel-Watt (dBW)

• Absolute level of power in decibels
• Value of 1 W is a reference defined to be 0 dBW
• Example
• Power of 1000 W is 30 dBW
• Power of 1 mW is 30 dBW

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Decibel Difference in Voltage

• Decibel is used to measure difference in voltage.
• Power PV2/R
• Decibel-millivolt (dBmV) is an absolute unit with
  0 dBmV equivalent to 1mV.
• Used in cable TV and broadband LAN

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Fourier Analysis
Signals
Aperiodic
Periodic (fo)
Discrete Continuous
Discrete Continuous
DFS
FS
FT
Finite time
Infinite time
DTFT
DFT
FT Fourier Transform DFT Discrete Fourier
Transform DTFT Discrete Time Fourier
Transform FS Fourier Series DFS Discrete
Fourier Series
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Fourier Series

• Any periodic signal can be represented as sum of
  sinusoids, known as Fourier Series

fundamental frequency
DC Component
If A0 is not 0, x(t) has a DC component
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Fourier Series

• Amplitude-phase representation

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Fourier Series Representation of Periodic Signals
- Example
x(t)
1
1/2
-1/2
1
3/2
-3/2
-1
2
-1
T
Note (1) x( t)x(t) ? x(t) is an even
function (2) f0 1 / T ½
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Fourier Series Representation of Periodic Signals
- Example
Replacing t by t in the first integral sin(-2pnf
t) - sin(2pnf t)
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Fourier Series Representation of Periodic Signals
- Example
Since x( t)x(t) as x(t) is an even function,
then Bn 0 for n1, 2, 3,
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Another Example
x1(t)
1
1
-1
2
-2
-1
T
Note that x1(-t) -x1(t) ? x(t) is an odd function
Also, x1(t)x(t-1/2)
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Another Example
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Fourier Transform

• For a periodic signal, spectrum consists of
  discrete frequency components at fundamental
  frequency its harmonics.
• For an aperiodic signal, spectrum consists of a
  continuum of frequencies.
• Spectrum can be defined by Fourier transform
• For a signal x(t) with spectrum X(f), the
  following relations hold

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Fourier Transform Example
x(t)
A
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Fourier Transform Example
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Signal Power

• A function x(t) specifies a signal in terms of
  either voltage or current
• Instantaneous power of a signal is related to
  average power of a time-limited signal, and is
  defined as
• For a periodic signal, the average power in one
  period is

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Power Spectral Density Bandwidth

• Absolute bandwidth of any time-limited signal is
  infinite.
• Most power in a signal is concentrated in finite
  band.
• Effective bandwidth is the spectrum portion
  containing most of the power.
• Power spectral density (PSD) describes power
  content of a signal as a function of frequency

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Power Spectral Density Bandwidth

• For a periodic signal, power spectral density is
• where ?(f) is

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Power Spectral Density Bandwidth

• For a continuous valued function S(f), power
  contained in a band of frequencies f1 lt f lt f2
• For a periodic waveform, the power through the
  first j harmonics is

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Power Spectral Density Bandwidth - Example

• Consider the following signal
• The signal power is

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Fourier Analysis Example

• Consider the half-wave rectified cosine signal
  from Figure B.1 on page 793
• Write a mathematical expression for s(t)
• Compute the Fourier series for s(t)
• Find the total power of s(t)
• Find a value of n such that Fourier series for
  s(t) contains 95 of the total power in the
  original signal
• Write an expression for the power spectral
  density function for s(t)

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Example (Cont.)

1. Mathematical expression for s(t)

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Example (Cont.)

• Fourier Analysis

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Example (Cont.)

• Fourier Analysis (cont.)

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Example (Cont.)

• Fourier Analysis (cont.)

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Example (Cont.)

• Fourier Analysis (cont.)

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Example (Cont.)

• Fourier Analysis (cont.)

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Example (Cont.)

• Fourier Analysis (cont.)

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Example (Cont.)

• Fourier Analysis (cont.)

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Example (Cont.)

• Total Power

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Example (Cont.)

• Finding n such that we get 95 of total power

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Example (Cont.)

• Finding n such that we get 95 of total power

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Example (Cont.)

• Finding n such that we get 95 of total power

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Example (Cont.)

• Power Spectral Density function (PSD)
• Or more accurately

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Example (Cont.)

• Power Spectral Density function (PSD)

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Signal with DC Component
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Data Rate and Bandwidth

• Any transmission system has a limited band of
  frequencies
• This limits the data rate that can be carried
• Example on pages 65 66

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Analog and Digital Data Transmission

• Data
• Entities that convey meaning
• Signals
• Electric or electromagnetic representations of
  data
• Transmission
• Communication of data by propagation and
  processing of signals

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Analog and Digital Data

• Analog
• 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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Analog and Digital Signals

• Means by which data are propagated
• Analog
• 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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Advantages Disadvantages of Digital

• Cheaper
• Less susceptible to noise
• Greater attenuation
• Pulses become rounded and smaller
• Leads to loss of information

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Attenuation of Digital Signals
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Components of Speech

• Frequency range (of hearing) 20Hz-20kHz
• Speech 100Hz-7kHz
• Easily converted into electromagnetic signal for
  transmission
• Sound frequencies with varying volume converted
  into electromagnetic frequencies with varying
  voltage
• Limit frequency range for voice channel
• 300-3400Hz

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Conversion of Voice Input into Analog Signal
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Video Components

• USA - 483 lines scanned per frame at 30 frames
  per second
• 525 lines but 42 lost during vertical retrace
• So 525 lines x 30 scans 15750 lines per second
• 63.5?s per line
• 11?s for retrace, so 52.5 ?s per video line
• Max frequency if line alternates black and white
• Horizontal resolution is about 450 lines giving
  225 cycles of wave in 52.5 ?s
• Max frequency of 4.2MHz

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Binary Digital Data

• From computer terminals etc.
• Two dc components
• Bandwidth depends on data rate

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Conversion of PC Input to Digital Signal
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Data and Signals

• Usually use digital signals for digital data and
  analog signals for analog data
• Can use analog signal to carry digital data
• Modem
• Can use digital signal to carry analog data
• Compact Disc audio

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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 Transmission

• Analog signal transmitted without regard to
  content
• May be analog or digital data
• Attenuated over distance
• Use amplifiers to boost signal
• Also amplifies noise

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Digital Transmission

• Concerned with content
• Integrity endangered by noise, attenuation etc.
• Repeaters used
• Repeater receives signal
• Extracts bit pattern
• Retransmits
• Attenuation is overcome
• Noise 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
• High bandwidth links economical
• High degree of multiplexing easier with digital
  techniques
• Security Privacy
• Encryption
• Integration
• Can treat analog and digital data similarly

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Transmission Impairments

• Signal received may differ from signal
  transmitted
• Analog - degradation of signal quality
• Digital - bit errors
• Caused by
• Attenuation and attenuation distortion
• Delay distortion
• Noise

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Attenuation

• Signal strength falls off with distance
• Depends on medium
• Received signal strength
• must be enough to be detected
• must be sufficiently higher than noise to be
  received without error
• Attenuation is an increasing function of
  frequency

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Delay Distortion

• Only in guided media
• Propagation velocity varies with frequency

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Noise (1)

• Additional signals inserted between transmitter
  and receiver
• Thermal
• Due to thermal agitation of electrons
• Uniformly distributed
• 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
• Impulse
• Irregular pulses or spikes
• e.g. External electromagnetic interference
• Short duration
• High amplitude

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More on Thermal (White) Noise

• Power of thermal noise present in a bandwidth B
  (Hz) is given by
• T is absolute temperature in kelvin and k is
  Boltzmanns constant
• k 1.38?10-23 J/K

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Channel Capacity

• Data 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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Nyquist Bandwidth

• If rate of signal transmission is 2B then signal
  with frequencies no greater than B is sufficient
  to carry signal rate
• Given bandwidth B, highest signal rate is 2B
• Given binary signal, data rate supported by B Hz
  is 2B bps
• Can be increased by using M signal levels
• C 2B log2M

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Shannon Capacity Formula

• Consider data rate,noise and error rate
• Faster data rate shortens each bit so burst of
  noise affects more bits
• At given noise level, high data rate means higher
  error rate
• Signal to noise ratio (in decibels)
• SNRdB10 log10 (signal/noise)
• Capacity CB log2(1SNR)
• This is error free capacity

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Eb/N0

• Determines digital data rates and error rates
• Standard quality measure for digital
  communication system performance
• Ratio of signal energy per bit to noise power
  density per Hertz
• Eb energy per bit in a signal (Joules) STb,
  where S signal power (Watts), Tb time
  required to send 1 bit (seconds) ? R bit rate
  1/ Tb

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Eb/N0 (Cont.)

• Bit error rate for digital data is a decreasing
  function of Eb/N0
• ? Given Eb/N0 to achieve a desired error rate,
  parameters in formula above may be selected
• Eb/N0 does not depend on bandwidth (vs. SNR)
• N N0BT ?

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Eb/N0 (Cont.)

• Shannons result can be rewritten as
• Relates achievable spectral efficiency C/B to
  Eb/N0