Data Transmission

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Data Transmission

• Lesson 3
• NETS2150/2850

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Lesson Outline

• Understand the properties a signal
• Explain the difference of Data vs Signal
• Understand the influence of attenuation, delay
  distortion and noise on signal propagation
• Appreciation of unit of decibel

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Position of the physical layer
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To be transmitted, data must be transformed to
electromagnetic signals
Signals can be analogue or digital. Analogue
signals can have an infinite number of values in
a range Digital signals can have only a limited
number of values.
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Signals

• Analogue 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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In data communication, we commonly use periodic
analogue signals and aperiodic digital signals.
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A Sine Wave
s(t) A sin(2?ft ?)
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Sine Wave

• Peak Amplitude - A
• maximum strength of signal
• In volts (V)
• Frequency - f
• Rate of change of signal
• Hertz (Hz) or cycles per second
• Period time for one repetition (T)
• T 1/f
• Phase - ? (in degree or radian)
• the position of the waveform relative to time
  zero
• How far from origin when voltage change from -ve
  to ve

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Amplitude
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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.
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Period and frequency
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Frequency and period are inverses of each other
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Table 3.1 Units of periods and frequencies
Unit Equivalent Unit Equivalent
Seconds (s) 1 s hertz (Hz) 1 Hz
Milliseconds (ms) 103 s kilohertz (KHz) 103 Hz
Microseconds (?s) 106 s megahertz (MHz) 106 Hz
Nanoseconds (ns) 109 s gigahertz (GHz) 109 Hz
Picoseconds (ps) 1012 s terahertz (THz) 1012 Hz
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Example
Express a period of 100 ms in microseconds, and
express the corresponding frequency in kilohertz
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If a signal does not change at all, its frequency
is zero If a signal changes instantaneously, its
frequency is infinite
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Relationships between different phases
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Example
A sine wave is offset one-sixth of a cycle with
respect to time zero. What is its phase in
degrees and radians?
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Sine wave examples
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Sine wave examples (continued)
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Wavelength

• Distance occupied by one cycle (in meters)
• ?
• Assuming signal velocity v
• ? vT
• ?f v
• c 3108 ms-1 (speed of light in free space)

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An analogue signal is best represented in the
frequency domain
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Time and frequency domains
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A single-frequency sine wave is not useful in
data communications we need to change one or
more of its characteristics to make it useful.
When we change one or more characteristics of a
single-frequency signal, it becomes a composite
signal made of many frequencies.
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According to Fourier analysis, any composite
signal can be represented as a combination of
simple sine waves with different frequencies,
phases, and amplitudes.
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Three odd harmonics
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Adding first three harmonics
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Frequency spectrum comparison
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Analogue and Digital Data Transmission

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

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Analogue and Digital Data

• Analogue
• Continuous values within some interval
• e.g. sound
• Digital
• Discrete values
• e.g. text, integers

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Analogue and Digital Signals

• Means by which data are propagated
• Analogue
• Continuously variable
• Speech range 100Hz to 7kHz
• Telephone range 300Hz to 3400Hz
• Video bandwidth 4MHz
• Digital
• Use two DC components

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Advantages Disadvantages of Digital

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

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Attenuation of Digital Signals
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Data vs Signal
Analogue
Analogue
Analogue
Analogue
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Analogue Transmission

• Analogue signal transmitted without regard to
  content
• May be analogue or digital data
• Attenuated over distance
• Use amplifiers to boost signal
• But this also amplifies noise

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Digital Transmission

• Concerned with content
• Integrity endangered by noise, attenuation etc.
• Repeaters used
• Repeater extracts bit pattern from received
  signal and retransmits
• Attenuation is overcome
• Noise is not amplified

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Advantages of Digital Transmission

• Digital technology
• Low cost LSI/VLSI technology (smaller)
• 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

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Transmission Impairments

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

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Attenuation and Dispersion (Delay Distortion)
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Attenuation

• Signal strength falls off with distance
• Depends on type of 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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Signal corruption
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Delay Distortion

• Propagation velocity varies with frequency
• Different signal component travel at different
  rate resulting in distortion

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Noise

• Additional unwanted signals inserted between
  transmitter and receiver
• e.g. thermal noise, crosstalk etc.

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Spectrum Bandwidth

• Spectrum
• range of frequencies contained in signal
• Bandwidth
• width of spectrum
• band of frequencies containing most of the energy

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Bandwidth
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Example
If a periodic signal is decomposed into five sine
waves with frequencies of 100, 300, 500, 700,
and 900 Hz, what is the bandwidth? Draw the
spectrum, assuming all components have a maximum
amplitude of 10 V.
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Example
A signal has a bandwidth of 20 Hz. The highest
frequency is 60 Hz. What is the lowest frequency?
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Example
A signal has a spectrum with frequencies between
1000 and 2000 Hz (bandwidth of 1000 Hz). A medium
can pass frequencies from 3000 to 4000 Hz (a
bandwidth of 1000 Hz). Can this signal faithfully
pass through this medium?
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A digital signal
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Figure 3.17 Bit rate and bit interval
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Example
A digital signal has a bit rate of 2000 bps. What
is the duration of each bit (bit interval)
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A digital signal is a composite signal with an
infinite bandwidth
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Baud rate and bit-rate

• bit rate is the number of bits transmitted per
  second
• baud rate is the number of signal units per
  second required to represent bits
• An important measure in data transmission
• Represents how efficiently we move data from
  place to place
• Equals bit rate divided by the number of bits
  represented by each signal shift

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Baud rate and bit-rate (2)
2-level signal
VS
One signal element conveys 1 bit
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Channel capacity and Nyquist Bandwidth

• Given bandwidth B Hz, highest signal rate is 2B
• For binary signal, data rate supported by B Hz is
  2B bps in a noiseless channel
• Can be increased by using M signal levels
• C 2B log2M

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Example

• Assume voice channel (range 300-3400 Hz)
• Thus, bandwidth is 3100 Hz (i.e. B)
• This translates to capacity of 2B 6200 bps
• If M 8 signal levels (3-bit word), capacity
  becomes 18,600 bps (2Blog2M)

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Decibels (dB)

• A measure of ratio between two signal levels
• Gain is given by
• GdB 10 log10 Pout dB
• Pin
• When gain is ve, this means loss or attenuation
• Example 1 Pin 100mW, Pout 1 mW
• Gain 10 log10 (1/100) -20 dB
• implies attenuation is 20 dB

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Shannon Capacity Formula

• This considers data rate, noise and error rate in
  the channel
• 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 (SNR)
• Thus, Shannons formula is
• C B log2(1SNR)
• Represents theoretical max capacity!

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Example

• Assume spectrum of a channel is between 3 MHz and
  4 MHz and the SNR is 24 dB
• B 4 3 1 MHz
• SNRdB 24 dB 10log10(SNR)
• ? SNR 251
• Thus, C B log2(1SNR) 106 ? log2(1251)
• ? 8 ? 106 8 Mbps

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Example
Consider an extremely noisy channel in which the
value of the signal-to-noise ratio is almost
zero. In other words, the noise is so strong that
the signal is faint. For this channel the
capacity is calculated as
C B log2 (1 SNR) B log2 (1 0) B log2
(1) B ? 0 0
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Example
We can calculate the theoretical highest bit rate
of a regular telephone line. A telephone line
normally has a bandwidth of 3000 Hz (300 Hz to
3300 Hz). The signal-to-noise ratio is usually
3162. For this channel the capacity is calculated
as
C B log2 (1 SNR) 3000 log2 (1 3162)
3000 log2 (3163) C 3000 ? 11.62 34,860 bps
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Example
We have a channel with a 1 MHz bandwidth. The SNR
for this channel is 63 what is the appropriate
bit rate and signal level?
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Summary

• Analogue vs Digital Transmission
• Transmission Impairments of a signal
• Nyquist Formula to estimate channel capacity in a
  noiseless environment
• Shannon Capacity Formula estimates the upper
  limit of capacity with noise effect
• Next Transmission Media