Computer Networks

Digitization

Spring 2006 Computer Networks 2

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.

t

s(t) Signal at the sender (original)

t

NoiseNoise

Signal at the receiver

Spring 2006 Computer Networks 3

Why we are going digital?s(t) Signal at the

sender (original)

Noise

Signal with noise

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.

r(t) Signal at the receiver

Spring 2006 Computer Networks 4

Digital versus Analog Transmission

Advantages of digital communication Regenerator receiver

Different kinds of digital signal are treated identically

Propagation distance

Originalpulse

Regeneratedpulse

DataVoice

MediaA bit is a bit!

Spring 2006 Computer Networks 5

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

Spring 2006 Computer Networks 6

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.

Spring 2006 Computer Networks 7

CODEC

Codec t

V

t

V

CODer-DECoder

Spring 2006 Computer Networks 8

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 .

Spring 2006 Computer Networks 9

Sampling – Example

s(t)

t

s1 (t)

t

Analog signal Samples from the analog signal

Spring 2006 Computer Networks 10

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

Spring 2006 Computer Networks 11

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+100 +75 +50 +25 0 -25 -50 -75-100-125

+24+38

+48+39

+26

-15

-50

-80

+102+110

+125+105

+88

10110010-50

1101000-80

10001111-015

01011000+8500011010+26

01101001+10500100111+39

01111101+12400110000+048

01101110+11000100110+038

01100100+10200011000+024

Sign bit+ is 0 , - is 1

Spring 2006 Computer Networks 12

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.

Spring 2006 Computer Networks 13

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

Spring 2006 Computer Networks 14

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