Pulse Code Modulation

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Pulse Code Modulation

• The advantages of digital communication systems
  (cf. analogue communication)
• Easier to store as a pattern of 1's and 0's
• Increased Immunity
• non-linearities
• Easier to process in computers and digital signal
  processors
• Can be coded for security and error correction
  purposes
• Several digital signals can easily be interleaved
  (multiplexed) and transmitted on one channel
• Noisy digital signals can be regenerated more
  effectively than analogue signals can be
  amplified.

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A brief aside about ADCs

• ADCs are used to convert an analogue input
  voltage into a number that can be interpreted as
  a physical parameter by a computer.

0000
0110
0111
0011
1100
1001
1011
Numbers passed from ADC to computer to represent
analogue voltage
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Sampling

• The input signal is sampled prior to digitisation
  and an approximation to the input is
  reconstructed by the digital-to-analogue
  converter

input
Sampling
Digitisation
code, modulate

• Transmission
• Wire/optical fibre
• Aerial/free-space

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Sampling an analogue signal

• Prior to digitisation, signals must be sampled
• With a frequency fs2B1/T
• ADC converts the height of each pulse into binary
  representation
• Sampling involves the multiplication of the
  signal by a train of sampling pulses

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Sampling as multiplication by a sampling waveform

• Sampling pulse is short enough so that can
  normally considered have zero duration
• DAC, however produces pulses length T

• Multiplication Amplitude modulation
• Amplitude modulation produces sidebands

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• Sidebands produced by multiplication with a
  carrier
• That is, amplitude modulation

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• Sidebands at each harmonic of the sampling pulse
• Digital-to-analogue conversion involves recovery
  of the baseband
• How?
• What is the minimum value of fs for which there
  is no overlap of the Harmonics with the baseband?

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• If the sidebands do not overlap the signal can be
  recovered

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• Practical sampling
• the "Sample-and-hold" system
• This is Nyquists theorem
• For a signal of bandwidth B Hz, the minimum
  sampling rate is 2B samples/s

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• Effect of sampling rate
• sampling at more than the Nyquist Rate

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• Sampling at the Nyquist Rate
• cannot build an ideal filter -

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• Undersampling
• produces aliasing distortion!

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Aliasing-time domain
Oversampled signal
Reconstructed signal
Undersampled signal
Reconstructed signal
Samplingaliasing Nyquisttime domain
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• The Anti-alias (Pre-sampling) filter
• ensures that sampling obeys the Nyquist theorem

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Examples

• For the compact disc (Audio CD) the maximum
  signal frequency is 20 kHz and the sampling rate
  is 44.1 kHz.
• The Nyquist Sampling Rate is 40 kHz
• Hence the guard band is 4.1 kHz wide.
• In the telephone system (see Section 5.8), the
  speech signal has a bandwidth up to 3.4 kHz and a
  sampling rate of 8 kHz,
• The Nyquist Sampling Rate is 6.8 kHz
• Hence the guard band is 1.2 kHz wide.

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Regeneration v amplification

• Gain of amplifiers equals loss in transmission
  lines
• SNR analog S/kN
• SNR digital S/N
• In practice finite S/N means there will be a low
  level of bit errors
• Some accumulation of bit-error noise with
  repeaters, but much lower level than with
  analogue amplification

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• A Pulse-Code Modulation communication system
• "PCM"

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A digital communication system - "PCM"

• Anti-alias Filter
• Digitiser/Sample-and-Hold circuit
• Analogue-to-Digital Converter
• Coding-
• Source coding for data compression,
• Line coding for signalling efficiency
• Error coding to reduce the effect of errors
• Modulator
• Physical Channel (with repeaters if necessary)
• Copper cables
• Fibre Optic cables
• Radio
• Sonar
• Recording medium
• Demodulator
• Decoder (Source-, Line- and Error-)
• Digital-to-Analogue Converter
• Reconstruction Filter

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Time-division Multiplexing "TDM"

• Allocate interleaved time-slots to each signal
• Assemble the binary coded samples into Frames
• 2-channel time-division multiplexing scheme

• Two channels share a single physical channel
• Cost?

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The 32-channel PCM Transmission system

• 30 speech signals plus two control channels for
  signalling and synchronising
• Signal bandwidth 3.4 kHz
• Sampling rate 8 kHz
• Hence frame length?
• Sample size 8 bits/sample
• Hence bit rate from each signal 64 kbit/s
• 32 channels
• Hence each time slot 3.906 ?s
• 1/(800032)
• Overall data rate 2.048 Mbit/s
• 8000328

125 ?s
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• A number of frames can be time-division
  multiplexed together in a TDM heirachy.
• 4 frames of 32 channels
• 128 basic PCM channels,
• Has data rate of 4 x 2.048 Mbit/s 8.192
  Mbit/s
• 8.448Mbit/s including extra signalling bits
• 4 x 128 512 channels
• Has data rate 4 x8.192 Mbit/s ( signalling
  bits)
• 34.368 Mbit/s
• etc
• Up to a multiplex of 32768 channels with an
  overall data rate of 2.48832 Gbit/s.

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Spectrum of a train of pulses