Waves and Signals

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Waves and Signals
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Basics

• Signals and waves
• Different types of transmission
• Transmission media
• Voice telephony
• Data transmission and data networks
• How much, how fast and how far?

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Simple telegraphy (1840s)
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Signals

• signals can be analogue or digital
• analogue signals vary continuously and can take
  any value within some given range
• digital signals are chosen from a discrete
  (limited, finite) range of possibilities, e.g.
  0,1 or long, short or
• A - Z, 0 - 9

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Analogue signal
Voltage
Time
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Digital signal
Voltage
Time
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How signals get damaged
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Data

• data can be analogue or digital
• speech is an example of analogue data and text is
  an example of digital data
• digital data can be transmitted using analogue
  signals and vice-versa, using analogue-to-digital
  converters (ADC) or digital-to-analogue
  converters.

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Waves amplitude, frequency and phase
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Amplitude difference
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Frequency difference
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Phase difference
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Measuring frequency

• Frequency is measured in Hertz (cycles per
  second)
• 1 KiloHertz (1 KHz) is 1,000 Hz, i.e., 1,000
  cycles per second
• 1 MegaHertz (1MHz) is 1,000 KHz, i.e. a million
  cycles per second
• 1 GigaHertz (1GHz) is 1,000 MHz, i.e. a thousand
  million cycles per second.

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A little maths

• There are various tricks for helping us to do
  calculations with frequencies
• These are not particularly difficult its just a
  question of remembering the techniques

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Indices

• an means n as multiplied together
• 23 2 2 2 8
• 102 10 10 100
• Notice that
• 23 22 2 2 2 2 2 25
• 102 101 10 10 10 103

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Indices (cont)

• The general rule is
• am an amn
• So, if m 0,
• a0 an a0n an
• Hence we interpret a0 as 1.

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Indices (cont)

• This means
• 1 KHz 1,000 Hz 103 Hz
• 1 MHz 1,000 KHz 1,000,000 Hz 106 Hz
• 1 GHz 1,000 MHz 103 ? 106 Hz 109 Hz

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Indices (cont)

• Using the general rule again,
• 23 2-3 20 1
• so
• 2-3 1/23 1/8
• In general,
• a-n 1/an

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Indices (cont)

• This means
• am-n am a-n
• am 1/an am an
• for example,
• 22 25-3 25 23
• i.e.
• 4 32 8

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Small units of time

• 1millisecond (ms) 10-3seconds 1/1,000th of a
  second
• 1 microsecond (µs) 10-6 seconds 1/1,000,000th
  of a second
• 1 nanosecond (ns) 10-9 seconds
  1/1,000,000,000th of a second.

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Example 1

• A wave has a frequency of 10 MHz. How long does
  it take to complete one cycle?
• The wave performs 10,000,000 107 cycles per
  second. To complete one cycle, it therefore
  takes
• 1/10,000,000 secs 1/ 107 secs
• 10-7 secs 102 ? 10-9 secs 100 ns

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Example 2

• An electrical signal travels at a speed of 2?108
  metres per second in copper wire. How long does
  it take to go from one end to the other of a 1
  kilometre cable?
• Time Distance/Speed 1,000/(2?108 )
• 103/(2 ?108) 0.5?103?10-8 0.5?10-5 secs
• 5?10-6 secs 5 µs.

since 1 km 1,000 m
2-1 on the bottom becomes 21 on the top
Of course, you dont have to work it out this
way there are other ways!
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Exercise

• My favourite FM radio station broadcasts on 100
  MHz. Radio waves travel at the speed of light
  (3108 m/s). Given that the ideal length for the
  aerial is ¼ of the wavelength, how long should my
  aerial be?

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Answer to Exercise

• 100 MHz 108 Hz
• Therefore to complete one cycle it takes 1/108
  seconds 10-8 seconds (10 ns)
• Distance speedtime (rearranging formula from
  example 2)
• 108 3 10-8 100 3 3 metres
• ¼ of 3 metres is 75 cm
• Is your radio aerial the right length for your
  favourite station? Do the sums when you get back
  to your room!

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Why waves are important

• Any analogue signal can be represented as a
  combination of waves of different frequencies and
  amplitudes.
• Attenuation, dispersion and distortion affect
  different frequencies to a different extent.
• Each transmission medium has a range of
  frequencies that it can transmit with least
  damage.
• The most widely available network is the
  telephone network and this was designed to
  transmit analogue signals.

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Binary signals

• binary signals are digital signals with only two
  possible values, conventionally written 0 and 1
• binary signals are very widely used because they
  are technically easy to generate and to
  recognise
• any digital data can be represented as a sequence
  of binary signals.

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Bits and bytes

• a single binary signal is called a bit
• groups of eight bits are known as bytes
• bytes can be interpreted in many different ways
• in this course we shall usually interpret them as
  ASCII characters.

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ASCII (American Standard Code for Information
Interchange)

• a standard coding system that assigns a 7-bit
  code to each letter (separate codes for upper and
  lower case), digit, and punctuation character
• defined by the American National Standards
  Institute (ANSI)
• in practical use an extra bit, the parity bit is
  added as a check against errors.

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Vertical parity

• As a check that a byte has been transmitted
  correctly, channels require that all bytes have
  an odd number of 1s in them (odd parity systems)
  or an even number of 1s (even parity systems)
• the spare bit not used by the ASCII code is used
  as a parity bit and set to give the correct
  parity.

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Longitudinal parity

• Parity can also be applied to the same bit in
  each byte of a block. This is known as
  longitudinal parity (or longitudinal redundancy
  check).
• The combination of longitudinal and vertical
  parity means that single bit errors can be
  detected and corrected.

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Example

• 1011001101101111 0 odd longitudinal parity
  0011110011110100 0 even vertical parity
  1010101100000001 11111111110000110 0
• 0111110110000111 0
• 0001101011100100 01000000100000001 0
• 0011100101111110 1

1 complete byte
if rows add up to even, parity bit is 1,
otherwise 0
if columns add up to even, parity bit is 0,
otherwise 1
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Some ASCII codes