# Pulse Code Modulation Pulse Code Modulation • The

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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.
67
• 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

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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
–   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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