Computer Networks

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Computer Networks

• Digitization

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Transfer of an Analog Signal

• When analog data (voice, pictures, video) are
  transformed into analog electrical signal and
  transmitted through the media, the transmission
  impairments of the media change the signal.
• The noise is added to the signal and the result
  is a signal that does not look very much like the
  original.
• When the signal is amplified the noise is
  amplified, too.
• It is hard to extract the original signal.

s(t)
Signal at the sender (original)
Noise
Noise
t
Signal at the receiver
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Why we are going digital?
Signal at the sender (original)

• The receiver of the digital signal samples the
  received signal using the clock at the sender.
• It is only required that it detects whether the
  voltage is positive or negative.
• If positive it generates positive pulse
• If negative it generates negative pulse
• As a consequence the received signal is exactly
  the same as the one that was sent.
• Ocasionally errors can appear, but there are
  methods for their detection and correction.

s(t)
Noise
Signal with noise
Signal at the receiver
r(t)
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Digital versus Analog Transmission

• Advantages of digital communication
• Regenerator receiver
• Different kinds of digital signal are treated
  identically

Original pulse
Regenerated pulse
Propagation distance
Voice
Data
A bit is a bit!
Media
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Examples of Analog and Digital Transmission

• Analog transmission
• Local loop in PSTN (Public Switched Telephone
  Network)
• Cable television
• Digital Transmission
• Long-distance circuits in PSTN
• All kinds of LANs

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Analog-to-digital Conversion (A/D)

• Transformation of analog (continuous) signals
  into digital signals
• Infinite number of values of the amplitude need
  to be represented (coded) as a digital stream
  with a minimum loss of information
• The device that codes the analog signal into
  digital signal is called a coder. The device that
  performs the inverse operation is called a
  decoder. Both are usually assembled in one box
  called a codec.

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CODEC
V
V
Codec
t
t
CODer-DECoder
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Sampling the Analog Signal

• Nyquist Sampling Theorem
• Analog signal can be recovered if sampled at
  frequency equal or greater than its maximum
  frequency.
• In other words,
• If s(t) is a contnouus signal with a frequency
  spectum that stisfies S(f) fmax for all
  frequencies in S(F),
• then it can be recovered from a discrete signal
  consisting of samples taken from s(t) with
  frequency that is at least twice as big as fmax .

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Sampling Example
s(t)
s1 (t)
t
t
Samples from the analog signal
Analog signal
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Quantization

• Each sample obtained by the sampling process has
  a different amplitude.
• This would require an infinite number of values
  to be transmitted.
• To reduce the size of the problem the process of
  quantization is used.
• Quantization
• A method dividing the range of amplitude of the
  samples into finite number of levels,
• assigning sign and magnitude to each of these
  values, and
• Coding each of the levels with a binary equivalent

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Quantization - Example

• The range of amplitude is divided into 128
  negative and 128 positive levels (only some of
  them are shown on the diagram)
• The value of each sample is associated with one
  level
• Each level is translated into its seven-bit
  binary equivalent
• The sign of the level is translated into
  additional bit

125
125 100 75 50 25 0
01100100
102
00011000
024
110
105
102
88
01101110
110
00100110
038
48
01111101
124
00110000
048
38
39
26
24
01101001
105
00100111
39
01011000
85
00011010
26
-25 -50 -75 -100 -125
-15
10001111
-015
-50
1101000
-80
Sign bit is 0 , - is 1
-80
10110010
-50
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Quantization Error

• By replacing the value of the original sample
  with the value of the level, an intentional error
  called quantization error is introduced.
• Quantization error can be regarded as noise.
• The error depends on the number of levels used
• If 2N quantization levels are used, the number of
  bits per sample is N.
• More quantization level means lower quantization
  noise and more bits per sample.

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Pulse Code Modulation (PCM)

• The process of sampling, quantization, binary
  encoding and digita-to digital encoding is known
  as pulse code modulation
• PCM is usually used to transform voice signals.
• Voice data (phone conversation) is limited to
  below 4000Hz
• Require 8000 sample per second
• Each analog sample is assigned a digital value of
  8 bits.
• Therefore the speed of a digitized voice channel
  is 64 Kbps

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• Look at this presentation created by one of the
  former students. You can read more about how the
  voice is digitized and try the animation that
  shows the steps in the process of transforming
  the voice into a digital signal.
• Sampling the Voice