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Pulse Code Modulation Pulse Code Modulation • The

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Pulse Code Modulation Pulse Code Modulation • The Powered By Docstoc
					           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.
                                                            67
                 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.


0111                                                         Resolution=
0110                                                         1 part in 2n
0100
0101
0011
0010
0001
0000
1111
1110
1100
1010
1101
1011
1001

       0000   0110    0111   0011    1100   1001   1011

  Numbers passed from ADC to computer to represent analogue voltage
                                                                      68
                               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
                    Digital-to-analogue
       Filtering                            Demodulate, Decode
                        conversion

       output



                                                                           69
        Sampling an analogue signal
• Prior to digitisation, signals must be sampled
    – With a frequency fs=2B=1/T
• ADC converts the height of each pulse into binary representation
• Sampling involves the multiplication of the signal by a train of sampling
  pulses




                                                                              70
  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
                                                71
   – Amplitude modulation produces sidebands…
• Sidebands produced by multiplication with a
  carrier
  – That is, amplitude modulation
                                            72
•   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
                                                                                     73
       the baseband?
• If the sidebands do not overlap the signal   74
  can be recovered
• Practical sampling
  – the "Sample-and-hold" system:
• This is Nyquist’s theorem
  – For a signal of bandwidth B Hz, the minimum sampling
    rate is 2B samples/s                              75
• Effect of sampling rate
  – sampling at more than the Nyquist Rate   76
• Sampling at the Nyquist Rate
                                     77
  – cannot build an ideal filter -
• Undersampling –
  – produces aliasing distortion!   78
                      Aliasing-time domain


       Oversampled signal




      Reconstructed signal




       Undersampled signal




       Reconstructed signal                  79
Sampling:aliasing & Nyquist:time domain
• The Anti-alias
  (Pre-sampling)
  filter
  – ensures that
    sampling
    obeys the
    Nyquist
    theorem


                   80
                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.
                                            81
   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 lower82level
     than with analogue amplification
• A Pulse-Code Modulation communication
  system
  – "PCM"                             83
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*                  84
•   Reconstruction Filter*
       Time-division Multiplexing "TDM"
• Allocate interleaved time-slots to each signal
• Assemble the binary coded samples into Frames:
• 2-channel time-division multiplexing scheme:
     Frame n                 Frame n+1
     Slot 1      Slot 2      Slot 1      Slot 2
     Channel 1   Channel 2   Channel 1   Channel 2
     Sample 1    Sample 1    Sample 2    Sample 2




 • Two channels share a single physical channel      85
    – Cost?
 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? 125 s
  – Sample size 8 bits/sample
    • Hence bit rate from each signal 64 kbit/s
  – 32 channels
    • Hence each time slot 3.906 s
       – 1/(8000*32)
  – Overall data rate 2.048 Mbit/s
    • 8000*32*8                                   86
87
• 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.                                88
89
Spectrum of a train of pulses:




                                 90

				
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