Basics of Data Transmission

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Basics of Data Transmission

• Our Objective is to understand
• Signals, bandwidth, data rate concepts
• Transmission impairments
• Channel capacity
• Data Transmission

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Signals

• A signal is
• generated by a transmitter and transmitted over a
  medium
• function of time
• function of frequency, i.e., composed of
  components of different frequencies
• Analog signal
• varies smoothly with time
• E.g., speech
• Digital signal
• maintains a constant level for some period of
  time, then changes to another level
• E.g., binary 1s and 0s

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Periodic vs. Aperiodic Signals

• Periodic signal
• Pattern repeated over time
• s(tT) s(t)
• Aperiodic signal
• Pattern not repeated over time

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Sine Wave

• The fundamental periodic signal
• 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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Signals in Frequency Domain

• Signal is made up of many components
• Components are sine waves with different
  frequencies
• In early 19th century, Fourier proved that
• Any periodic function can be constructed as the
  sum of a (possibly infinite) number of sines and
  cosines

• This decomposition is called Fourier series
• f is called the fundamental frequency
• an, bn are amplitude of nth harmonic
• c is a constant

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Frequency Domain (contd)

• Fourier Theorem enables us to represent signal in
  Frequency Domain
• i.e., to show constituent frequencies and
  amplitude of signal at these frequencies
• Example 1 sine wave
• s(t) sin(2pft)

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Time and Frequency Domains Example 2
Time domain s(t)
Frequency domain S(f)
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Frequency Domain (contd)

• So, we can use Fourier theorem to represent a
  signal as function of its constituent
  frequencies,
• and we know the amplitude of each constituent
  frequency. So what?
• We know the spectrum of a signal, which is the
  range of frequencies it contains, and
• Absolute bandwidth width of the spectrum
• Q What is the bandwidth of the signal in the
  previous example? sin(2pft) sin(2p3ft)
• A 2f Hz

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Frequency Domain (contd)

• Q. What is the absolute bandwidth of square wave?

• Hint Fourier tells you that
• Absolute BW 8 (ooops!!)
• But, most of the energy is contained within a
  narrow band (why?)? we refer to this band as
  effective bandwidth, or just bandwidth

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Approximation of Square Wave
Using the first 3 harmonics, k1, 3, 5
A. BW 4f Hz
Using the first 4 harmonics, k1, 3, 5, 7
A. BW 6f Hz
Q. What is BW in each case?
Cool applet on Fourier Series
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Signals and Channels

• Signal
• can be decomposed to components (frequencies)
• spectrum range of frequencies contained in
  signal
• (effective) bandwidth band of frequencies
  containing most of the energy
• Communications channel (link)
• has finite bandwidth determined by the physical
  properties (e.g., thickness of the wire)
• truncates (or filters out) frequencies higher
  than its BW
• i.e., it may distort signals
• can carry signals with bandwidth channel
  bandwidth

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Bandwidth and Data Rate

• Data rate number of bits per second (bps)
• Bandwidth signal rate of change, cycles per sec
  (Hz)
• Well, are they related?
• Ex. Consider square wave with high 1 and low
  0 ?
• We can send two bits every cycle (i.e., during T
  1/f sec)
• Assume f 1 MHz (fundamental frequency) ? T 1
  usec
• Now, if we use the first approximation (3
  harmonics)
• BW of signal (5 f 1 f) 4 f 4 MHz
• Data rate 2 / T 2 Mbps
• So we need a channel with bandwidth 4 MHz to send
  at date rate 2 Mbps

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Bandwidth and Data Rate (contd)

• But, if we use the second approx. (4 harmonics)
• BW of signal (7 f 1 f) 6 f 6 MHz
• Data rate 2 / T 2 Mbps
• Which one to choose? Can we use only 2 harmonics
  (BW 2 MHz)?
• It depends on the ability of the receiver to
  discern the difference between 0 and 1
• Tradeoff cost of medium vs. distortion of signal
  and complexity of receiver

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Bandwidth and Data Rate (contd)

• Now, let us agree that the first appox. (3
  harmonics) is good enough
• Data rate of 2 Mbps requires BW of 4 MHz
• To achieve 4 Mbps, what is the required BW?
• data rate 2 (bits) / T (period) 4 Mbps ? T
  1 /2 usec
• ? f (fundamental freq) 1 /T 2 MHz ?
• BW 4 f 8 MHz
• Bottom line there is a direct relationship
  between data rate and bandwidth
• Higher data rates require more bandwidth
• More bandwidth allows higher data rates to be
  sent

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Bandwidth and Data Rate (contd)

• Nyquist Theorem (Assume noise-free channel)
• If rate of signal transmission is 2B then signal
  with frequencies no greater than B is sufficient
  to carry signal rate, OR alternatively
• Given bandwidth B, highest signal rate is 2B
• For binary signals
• Two levels ? we can send one bit (0 or 1) during
  each period ? data rate (C) 1 x signal rate 2
  B
• That is, data rate supported by B Hz is 2B bps
• For M-level signals
• M levels ? we can send log2M bits during each
  period ?
• C 2B log2M

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Bandwidth and Data Rate (contd)

• Shannon Capacity
• Considers data rate, (thermal) 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
• SNR Signal to noise ration
• SNR signal power / noise power
• Usually given in decibels (dB) SNRdB 10 log10
  (SNR)
• Shannon proved that C B log2(1 SNR)
• This is theoretical capacity, in practice
  capacity is much lower (due to other types of
  noise)

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Bandwidth and Data Rate (contd)

• Ex. A channel has B 1 MHz and SNRdB 24 dB,
  what is the channel capacity limit?
• SNRdB 10 log10 (SNR) ? SNR 251
• C B log2(1 SNR) 8 Mbps
• Assume we can achieve the theatrical C, how many
  signal levels are required?
• C 2 B log2M ? M 16 levels

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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 ? attenuation distortion

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Delay Distortion

• Only in guided media
• Propagation velocity varies with frequency
• Critical for digital data
• A sequence of bits is being transmitted
• Delay distortion can cause some of signal
  components of one bit to spill over into other
  bit positions ?
• intersymbol interference, which is the major
  limitation to max bit rate

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Noise (1)

• Additional signals inserted between transmitter
  and receiver
• Thermal
• Due to thermal agitation of electrons
• Uniformly distributed across frequencies ?
• 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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Data and Signals

• Data
• Entities that convey meaning
• Analog speech
• Digital text (character strings)
• Signals
• electromagnetic representations of data
• Analog continuous
• Digital discrete (pulses)
• Transmission
• Communication of data by propagation and
  processing of signals

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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
• But, it also amplifies noise!

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Digital Transmission

• Concerned with content
• Integrity endangered by noise, attenuation
• 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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Summary

• Signal composed of components (Fourier Series)
• Spectrum, bandwidth, data rate
• Shannon channel capacity
• Transmission impairments
• Attenuation, delay distortion, noise
• Data vs. signals
• Digital vs. Analog Transmission