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Computer Networks
Digitization
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.
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s(t)
Signal at the sender (original)
t
Noise
Noise
Signal at the receiver
2
t
Why we are going digital?
 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
r(t)
was sent.
s(t)
Signal at the sender
(original)
Noise
Signal with noise
Signal at the
receiver
 Ocasionally errors can appear, but there
are methods for their detection and
correction.
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Digital versus Analog Transmission
 Advantages of digital communication
 Regenerator receiver
Original
pulse
Regenerated
pulse
Propagation distance
 Different kinds of digital signal are treated identically
Voice
Data
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A bit is a bit!
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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
t
Codec
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
Analog signal
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t
Samples from the 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
+110 +105
+102
+100
+88
+75
+48
+50
+38 +39
+26
+25 +24
0
-15
-25
-50
-50
-75
-80
-100
+
-125
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Sign bit
is 0 , - is 1
+024
00011000
+102
01100100
+038
00100110
+110
01101110
+048
00110000
+124
01111101
+39
00100111
+105
01101001
+26
00011010
+85
01011000
-015
10001111
-80
1101000
-50
10110010
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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
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