Data Transmission

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• Data Transmission

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1. Terminology

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

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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 (f)
• Relative position in time

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Varying Sine Wavess(t) A sin(2pft f)
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Wavelength

• Distance occupied by one cycle
• Distance between two points of corresponding
  phase in two consecutive cycles
• ?wavelength
• Assuming signal velocity v
• ? vT
• ?f v
• c 2,98108 m/s (approximately 3108 m/s) 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)
sin(2pft)
(1/3) sin(2p(3f)t)
(4/p) sin(2pft)(1/3)sin(2p(3f)t)
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Spectrum Bandwidth

• Spectrum
• range of frequencies contained in signal
• Bandwidth (BW)
• Narrow band of frequencies containing most of the
  signal energy
• Absolute bandwidth Width of the spectrum
• Effective bandwidth (or bandwidth) energy of
  signal contained in a narrow band of frequencies
  (usually expressed as the 3 dB points)
• DC Component
• Component of zero frequency

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FrequencyDomainRepresentations
Signal spectrum
Absolute bandwidth 3f-1f2f
Fundamental frequency (f)
(4/p) sin(2pft)(1/3)sin(2p(3f)t)
This signal has an infinite bandwidth. Its
effective bandwidth is limited in a relatively
narrow band of frequencies where the most energy
of the signal is contained
s(t)1, -X/2lttltX/2
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Signal with DC Component
Time Domain
s(t) 1 (4/p) sin(2pft)(1/3)sin(2p(3f)t)
Frequency Domain
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Square wave
Square wave signal consists of an infinite number
of odd harmonics
(4/p) sin(2pft)(1/3)sin(2p(3f)t)(1/5)sin(2p(5f)
t)
(4/p) sin(2pft)(1/3)sin(2p(3f)t)(1/5)sin(2p(5f)
t) (1/7)sin(2p(7f)t)
(4/p)Ssin(2pkft)/k for odd k
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Data Rate and Bandwidth (1)

• Any transmission system has a limited band of
  frequencies
• This limits the data rate that can be carried

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Data Rate and Bandwidth (2)

• Suppose a digital transmission system is capable
  of transmitting signals with a BW of 4MHz. Let us
  attempt to transmit a square wave signal (i.e. a
  sequence of alternating 0s and 1s. What is the
  achievable data rate?

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Data Rate and Bandwidth (3)
Case 1 Assume that the square wave is
approximated to this signal.
(4/p) sin(2pft)(1/3)sin(2p(3f)t)(1/5)sin(2p(5f)
t)
BWfupper flower 5f f 4f If f1MHz, then
the BW4MHz. Since T1/f then signal period is
1/1MHz1µs Since one bit occurs every 0.5T then
Data rate1/0.5T2Mbps So, for this particular
example, for a BW of 4MHz, the Data Rate achieved
is 2Mbps
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Data Rate and Bandwidth (4)
Case 2 Assume that the square wave is
approximated to this signal.
(4/p) sin(2pft)(1/3)sin(2p(3f)t)(1/5)sin(2p(5f)
t)
BWfupper flower 5f f 4f If f2MHz, then
the BW8MHz. Since T1/f then signal period is
1/2MHz0.5µs Since one bit occurs every 0.5T then
Data rate1/0.5T4Mbps So, for this particular
example, for a BW of 8MHz, the Data Rate achieved
is 4Mbps
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Data Rate and Bandwidth (5)
Case 3 Assume that the square wave is
approximated to this signal.
(4/p) sin(2pft)(1/3)sin(2p(3f)t)
BWfupper flower 3f f 2f If f2MHz, then
the BW4MHz. Since T1/f then signal period is
1/2MHz0.5µs Since one bit occurs every 0.5T then
Data rate1/0.5T4Mbps So, for this particular
example, for a BW of 4MHz, the Data Rate achieved
is 4Mbps
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Data Rate and Bandwidth (6)

• Conclusions
• In general, any digital waveform has infinite BW
• If a digital waveform is transmitted over any
  medium, the transmission system will limit the BW
  that can be transmitted
• For any given medium, the greater the BW
  transmitted, the greater the cost
• Limiting the BW creates distortions, which makes
  the task of interpreting the received signal more
  difficult
• The more limited the BW, the greater the
  distortion, and the greater the potential for
  error by the receiver

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2. Analog and Digital Data Transmission

• Data
• Entities that convey information
• Signals
• Electric or electromagnetic representations of
  data
• Signaling is the physical propagation of the
  signal along a suitable medium
• 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)
(log scale)
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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 (binary 0 and 1)

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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 Analogue Signal
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Advantages of Digital Transmission

• Digital technology
• Low cost large-scale and very-large scale
  integration 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
• Economies of scale and convenience can be
  achieved by integrating voice, video and digital
  data

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3. Transmission Impairments

• Signal received may differ from signal
  transmitted
• For Analog signals - degradation of signal
  quality
• For Digital signals - bit errors may occur
• Most significant transmission impairments are
• Attenuation and attenuation distortion
• Delay distortion
• Noise

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Attenuation

• Signal strength reduces with distance over any
  transmission medium
• 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, i.e. the higher the frequency, the
  more the attenuation attenuation

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Delay Distortion (DD)

• Only in guided media
• It occurs because the propagation velocity of a
  signal through a guided medium varies with
  frequency
• Received signal is distorted due to varying
  delays experienced at its constituent frequencies
• DD is particularly critical for digital signals
• some of the signal components of one bit may
  spill over into other bit positions, causing
  intersymbol interference, which limits the
  maximum data rate over a transmission channel

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Noise (1)

• Additional signals inserted between transmitter
  and receiver
• Noise is the major limiting factor in
  communication system performance
• Noise can be divided into 4 main categories
• Thermal
• Intermodulation
• Crosstalk
• Impulse noise

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Noise (2)

• Thermal
• Due to thermal agitation of electrons in all
  electronic devices
• Uniformly distributed across the bandwidth
• Also referred to a white noise
• Intermodulation
• Signals that are the sum and difference of
  original frequencies sharing the same
  transmission medium
• Example mixing of signals at f1 and f2 may
  produce energy at f1f2, which could interfere
  with an intended signal at (f1f2) or (f1-f2)
• Crosstalk
• Unwanted coupling between signal paths
• Antennas or wires may pick up other unwanted
  signals, eg. phone line
• Impulse
• Non continuous, consisting of irregular pulses or
  noise spikes of short duration but of high
  amplitude
• e.g. External electromagnetic interference, such
  as lightning

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4. Channel Capacity

• As we have seen so far, there is a variety of
  impairments that distort or corrupt a signal. To
  what extent do these impairments limit the
  maximum achievable data rate?
• Channel Capacity is the maximum rate at which
  data can be transmitted over a communication
  channel.
• Data rate
• In bits per second (bps)
• Rate at which data can be communicated
• Bandwidth
• In cycles per second, or Hertz
• Constrained by transmitter and medium

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Nyquist Bandwidth

• Assume a noise-free channel
• If rate of signal transmission is 2B, then a
  signal with frequencies no greater than B is
  sufficient to carry signal rate
• or, given bandwidth B, highest signal rate is 2B
• Given a binary signal, the maximum data rate
  supported by a channel of bandwidth B Hz is 2B
  bps
• Maximum data rate, C, can be increased by using M
  signal levels
• Nyquist formula C 2 B log2M in bps
• However, receiver must be able to distinguish one
  of M possible signal elements. Noise and other
  transmission impairments limit the practical
  value of M.

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Shannon Capacity Formula

• Nyquists formula indicates that doubling BW,
  doubles the data rate in a noise-free channel.
• In practice, noise is always present. So, let us
  consider the relationship between data rate,
  noise and error rate.
• Faster data rate shortens each bit duration so a
  burst of noise affects more bits
• So, at a given noise level, the higher the data
  rate, the higher the error rate
• Signal-to-Noise ratio (SNR or S/N) expressed in
  decibels
• SNRdB10 log10 (Signal power/Noise power)
• Max channel Capacity is CB log2(1SNR) in bps
• This formula is for error-free capacity and
  assumes white noise. In practice, data rate is
  lower than C.

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