coe 342: data & computer communications (t042) dr. marwan abu-amara chapter 3: data transmission

COE 342: Data & Computer Communications (T042)Dr. Marwan Abu-Amara

Chapter 3: Data Transmission

COE 342 (T042) – Dr. Marwan Abu-

Amara 2

Agenda Concepts & Terminology Decibels and Signal Strength Fourier Analysis Analog & Digital Data Transmission Transmission Impairments Channel Capacity


Amara 3

Terminology (1) Transmitter Receiver Medium

Guided medium e.g. twisted pair, optical fiber

Unguided medium e.g. air, water, vacuum


Amara 4

Terminology (2) Direct link

No intermediate devices Point-to-point

Direct link Only 2 devices share link

Multi-point More than two devices share the link


Amara 5

Terminology (3) Simplex

One direction e.g. Television

Half duplex Either direction, but only one way at a time

e.g. police radio

Full duplex Both directions at the same time

e.g. telephone


Amara 6

Frequency, Spectrum and Bandwidth Time domain concepts

Analog signal Varies in a smooth way over time

Digital signal Maintains a constant level then changes to another

constant level Periodic signal

Pattern repeated over time Aperiodic signal

Pattern not repeated over time


Amara 7

Analogue & Digital Signals


Amara 8

PeriodicSignals


Amara 9

Sine Wave Peak Amplitude (A)

maximum strength of signal volts

Frequency (f) Rate of change of signal Hertz (Hz) or cycles per second Period = time for one repetition (T) T = 1/f

Phase () Relative position in time


Amara 10

Varying Sine Wavess(t) = A sin(2ft +)


Amara 11

Wavelength Distance occupied by one cycle Distance between two points of

corresponding phase in two consecutive cycles

Assuming signal velocity v

= vT f = v c = 3*108 m/sec (speed of light in free space)


Amara 12

Frequency Domain Concepts

Signal usually made up of many frequencies Components are sine waves Can be shown (Fourier analysis) that any

signal is made up of component sine waves Can plot frequency domain functions


Amara 13

Addition of FrequencyComponents(T=1/f)


Amara 14

FrequencyDomainRepresentations


Amara 15

Spectrum & Bandwidth Spectrum

range of frequencies contained in signal Absolute bandwidth

width of spectrum Effective bandwidth Often just bandwidth Narrow band of frequencies containing most of

the energy DC Component

Component of zero frequency


Amara 16

Decibels and Signal Strength Decibel is a measure of ratio between two

signal levels NdB = number of decibels

P1 = input power level

P2 = output power level

Example: A signal with power level of 10mW inserted onto a

transmission line Measured power some distance away is 5mW Loss expressed as NdB =10log(5/10)=10(-0.3)=-3 dB

1

210log10

P

PNdB


Amara 17

Decibels and Signal Strength Decibel is a measure of relative, not absolute, difference

A loss from 1000 mW to 500 mW is a loss of 3dB A loss of 3 dB halves the power A gain of 3 dB doubles the power

Example: Input to transmission system at power level of 4 mW First element is transmission line with a 12 dB loss Second element is amplifier with 35 dB gain Third element is transmission line with 10 dB loss Output power P2

(-12+35-10)=13 dB = 10 log (P2 / 4mW)

P2 = 4 x 101.3 mW = 79.8 mW


Amara 18

Relationship Between Decibel Values and Powers of 10 Power Power

RatioRatiodBdB Power Power

RatioRatiodBdB

101 10 10-1 -10

102 20 10-2 -20

103 30 10-3 -30

104 40 10-4 -40

105 50 10-5 -50

106 60 10-6 -60


Amara 19

Decibel-Watt (dBW) Absolute level of power in decibels Value of 1 W is a reference defined to be 0 dBW

Example: Power of 1000 W is 30 dBW Power of 1 mW is –30 dBW

W

PowerPower W

dBW 1log10 10


Amara 20

Decibel & Difference in Voltage Decibel is used to measure difference in

voltage. Power P=V2/R

Decibel-millivolt (dBmV) is an absolute unit with 0 dBmV equivalent to 1mV. Used in cable TV and broadband LAN

1

22

1

22

1

2 log20/

/log10log10

V

V

RV

RV

P

PNdB

mV

VoltageVoltage mV

dBmV 1log20


Amara 21

Fourier AnalysisSignals

Periodic (fo) Aperiodic

Discrete Continuous Discrete Continuous

DFS FS

DTFT

FT

DFT

Infinite time Finite time

FT : Fourier TransformDFT : Discrete Fourier TransformDTFT : Discrete Time Fourier TransformFS : Fourier SeriesDFS : Discrete Fourier Series


Amara 22

Fourier Series Any periodic signal can be represented as sum

of sinusoids, known as Fourier Series

1

000 )2sin()2cos(

2)(

nnn tnfBtnfA

Atx

T

dttxT

A0

0 )(2

T

n dttnftxT

A0

0 )2cos()(2

T

n dttnftxT

B0

0 )2sin()(2

If A0 is not 0,x(t) has a DC component

DC Component

fundamental frequency


Amara 23

Fourier Series Amplitude-phase representation

1

00 )2cos(

2)(

nnn tnfC

Ctx

00 AC 22nnn BAC

n

nn A

B1tan


Amara 24


Amara 25

Fourier Series Representation of Periodic Signals - Example

1

-1

1/2-1/2 1 3/2-3/2 -1 2

T

0111212)(2)(2

2)(

2 1

2/1

2/1

0

1

0

2

00

0 dtdtdttxdttxdttxT

AT

x(t)

Note: (1) x(– t)=x(t) x(t) is an even function(2) f0 = 1 / T = ½


Amara 26

Fourier Series Representation of Periodic Signals - Example

1

0

0

2/

0

0

0

0 )2cos()(2)2cos()(4

)2cos()(2

dttnftxdttnftxT

dttnftxT

ATT

n

2sin

4)2cos(2)2cos(2

1

2/1

0

2/1

0

0

n

ndttnfdttnf

2/

2/

0

0

0 )2sin()(2

)2sin()(2 T

T

T

n dttnftxT

dttnftxT

B

2/

0

0

0

2/

0 )2sin()(2

)2sin()(2 T

T

dttnftxT

dttnftxT

2/

0

0

2/

0

0 )2sin()(2

)2sin()(2 TT

dttnftxT

dttnftxT

Replacing t by –tin the first integralsin(-2nf t)=- sin(2nf t)


Amara 27

Fourier Series Representation of Periodic Signals - ExampleSince x(– t)=x(t) as x(t) is an even function, then

Bn = 0 for n=1, 2, 3, …

1

000 )2sin()2cos(

2)(

nnn tnfBtnfA

Atx

tnn

ntx

n

cos2

sin4

)(1

4 4 4 4( ) cos cos3 cos5 cos 7 ...

3 5 7x t t t t t

4 1 1 1( ) cos cos3 cos5 cos 7 ...

3 5 7x t t t t t


Amara 28

Another Example

1

-1

1-1 2

T

-2

x1(t)

Note that x1(-t)= -x1(t) x(t) is an odd function

Also, x1(t)=x(t-1/2)

2

17 cos

7

1

2

15 cos

5

1

2

13 cos

3

1

2

1 cos

4)(1 tttttx


Amara 29

Another Example

2

77 cos

7

1

2

55 cos

5

1

2

33 cos

3

1

2 cos

4)(1

tttttx

7in

7

1 5sin

5

1 3in

3

1 in

4)(1 tsttststx

tt sin2

cos

tt 3sin

2

33 cos

tt 5sin2

55 cos

tt 7sin

2

77 cos


Amara 30

Fourier Transform For a periodic signal, spectrum consists of

discrete frequency components at fundamental frequency & its harmonics.

For an aperiodic signal, spectrum consists of a continuum of frequencies. Spectrum can be defined by Fourier transform For a signal x(t) with spectrum X(f), the following

relations hold

dfefXtx ftj 2 )()(

dtetxfX ftj 2 )()(


Amara 31


Amara 32

Fourier Transform Example

x(t)A

22

dtetxfX ftj 2 )()(

2/

2/

22/

2/

2

2 )(

ftjftj efj

AdteAfX


Amara 33

Fourier Transform Example

2/2

)2/2sin(

2

2

2

2

22

2 2/22/2

f

ff

f

A

j

ee

f

A fjfj

f

fA

f

fAfX

)sin(

2/2

)2/2sin()(

j

ee jj

2sin

2cos

jj ee


Amara 34

Signal Power A function x(t) specifies a signal in terms of

either voltage or current Instantaneous power of a signal is related to

average power of a time-limited signal, and is defined as

For a periodic signal, the average power in one period is

2)(tx2

2

1

1( )

2 1

t

t

x t dtt t

T

dttxT

0

2)(

1


Amara 35

Power Spectral Density & Bandwidth Absolute bandwidth of any time-limited signal is

infinite. Most power in a signal is concentrated in finite

band. Effective bandwidth is the spectrum portion

containing most of the power. Power spectral density (PSD) describes power

content of a signal as a function of frequency


Amara 36

Power Spectral Density & Bandwidth For a periodic signal, power spectral density

is

where (f) is

2

0( ) ( )nn

PSD f C f nf

1 =00 0( ) f

ff


Amara 37

Power Spectral Density & Bandwidth For a continuous valued function S(f), power

contained in a band of frequencies f1 < f < f2

For a periodic waveform, the power through the first j harmonics is

2

1

)(2f

f

dffSP

j

nnCCP

1

220 2

125.0


Amara 38

Power Spectral Density & Bandwidth - Example Consider the following signal

The signal power is

7in

7

1 5sin

5

1 3in

3

1 in)( tsttststx

watt586.0 49

1

25

1

9

11

2

1

Power


Amara 39

Fourier Analysis Example Consider the half-wave rectified cosine signal from

Figure B.1 on page 793:1. Write a mathematical expression for s(t)

2. Compute the Fourier series for s(t)

3. Find the total power of s(t)

4. Find a value of n such that Fourier series for s(t) contains 95% of the total power in the original signal

5. Write an expression for the power spectral density function for s(t)


Amara 40

Example (Cont.)1. Mathematical expression for s(t):

cos(2 ) , -T/4 T/40 , T/4 3T/4( ) oA f t t

ts t


Amara 41

Example (Cont.)2. Fourier Analysis:

1 )2/sin( where, 2

)2/sin(2)2/sin()2/sin(

)2/sin()2/sin(/2

)/2sin(2

)2cos(2

)(2

4/

4/

4/

4/

4/

4/

0

A

AA

A

T

Tt

T

A

dttfT

Adtts

TA

T

T

T

T

o

T

T


Amara 42

Example (Cont.)2. Fourier Analysis (cont.):

/ 4 / 4

/ 4 / 4

/ 4

/ 4

2 2( )cos(2 ) cos(2 )cos(2 )

sin(2 ( 1) ) sin(2 ( 1) )2 , for 1

4 ( 1) 4 ( 1)

cos( / 2) cos( / 2) , for

( 1) ( 1)

T T

n o o o

T T

T

o o

o o T

AA s t nf t dt f t nf t dt

T T

n f t n f tAn

T n f n f

A n nn

n n

1

2

sin( ) sin( ) cos( )cos( ) , and

2( ) 2( )

sin( ) cos(

Note:

)

ax bx ax bxax bx dx

a b a b

x x


Amara 43


2 2

2 2

2

( ) ( )

( ) ( )

( )

2

0 , for and 1

( 1) ( 1)

( 1) ( 1)

( 1) ( 1) ( 1)( 1) ( 1)

( 1)( 1)

( 1) ( 1) ( 1)( 1)

( 1)

oddn n

n n

n

n

n

A n n

AA

n n

A n n

n n

An n

n

2(1 )

2

2 ( 1) , for

( 1)even

n

An

n


Amara 44


/ 4 / 4

1

/ 4 / 4

/ 42

/ 4

/ 4

/ 4

2 2( )cos(2 1 ) cos(2 )cos(2 )

2 cos (2 )

sin(4 )2 2 sin( ) sin( )

2 4 2 4 8

2

T T

n o o o

T T

T

o

T

T

o

o oT

AA s t f t dt f t f t dt

T T

Af t dt

T

f tA t A T

T f T f

A


Amara 45


/ 4 / 4

/ 4 / 4

/ 4

/ 4

2 2( )sin(2 ) cos(2 )sin(2 )

cos(2 ( 1) ) cos(2 ( 1) )2 , for 1

4 ( 1) 4 ( 1)

0

T T

n o o o

T T

T

o o

o o T

AB s t nf t dt f t nf t dt

T T

n f t n f tAn

T n f n f

, for 1n

cos( ) cos( ) sin( )cos(Note

): )

2( 2( )

ax bx ax bxax bx dx

a b a b


Amara 46


/ 4 / 4

1

/ 4 / 4

/ 4

/ 4

/ 4

/ 4

2 2( )sin(2 1 ) cos(2 )sin(2 )

sin(4 )

cos(4 ) cos( ) cos( )4 4

0

T T

n o o o

T T

T

o

T

T

o T

AB s t f t dt f t f t dt

T T

Af t dt

T

A Af t


Amara 47


2

2

1

(1 )

22,4,6,...

o 1

(1 )

2

( ) cos(2 ) sin(2 )2

2 ( 1) cos(2 ) cos(2 )

2 1

2C ,

20 , is odd and 1

2 ( 1) , 2, 4,

( 1)

n

n

on o n o

n

o on

n

n

As t A nf t B nf t

A A Af t nf t

n

A AC

C n n

AC n

n

6,...


Amara 48

Example (Cont.)3. Total Power:

3 / 4 / 422 2

/ 4 / 4

/ 42

/ 4

2

1( ) cos (2 )

sin(4 )

2 8

4

T T

s o

T T

T

o

o T

AP s t dt f t dt

T T

f tA t

T f t

A


Amara 49

Example (Cont.)4. Finding n such that we get 95% of total power:

2 2 220

0 2 2

2

2

For

40.1014

4 4

0.1014% 40.5%

0.25

0

n

C A APSD A

APower

A

n


Amara 50


2 2 2 220 1

1 2

2

2

For

0.2264 2 8

0.226% 90.5%

0.

1

25

n

C C A APSD A

APower

n

A


Amara 51


2 2 2 2 2 220 1 2

2 2 2

2

2

For

20.2485

4 2 2 8 9

0.2485% 99.41

2

2

0. 5%

n

C C C A A APSD A

AP wer

A

n

o


Amara 52

Example (Cont.)5. Power Spectral Density function (PSD):

Or more accurately:

220

1

1

4 2 nn

CPSD C

220

1

1( ) ( )

4 2 n on

CPSD f C f nf


Amara 53

Example (Cont.)5. Power Spectral Density function (PSD):

220

1

2 2 2

2 2 2 22,4,6,...

1( ) ( )

4 2

( )2 ( ) ( )

8 ( 1)

n on

oo

n

CPSD f C f nf

f nfA A Af f f

n


Amara 54

Signal with DC Component


Amara 55

Data Rate and Bandwidth

Any transmission system has a limited band of frequencies

This limits the data rate that can be carried Example on pages 65 & 66


Amara 56

Analog and Digital Data Transmission Data

Entities that convey meaning Signals

Electric or electromagnetic representations of data Transmission

Communication of data by propagation and processing of signals


Amara 57

Analog and Digital Data Analog

Continuous values within some interval e.g. sound, video

Digital Discrete values e.g. text, integers


Amara 58

Acoustic Spectrum (Analog)


Amara 59

Analog and Digital Signals Means by which data are propagated Analog

Continuously variable Various media

wire, fiber optic, space Speech bandwidth 100Hz to 7kHz Telephone bandwidth 300Hz to 3400Hz Video bandwidth 4MHz

Digital Use two DC components


Amara 60

Advantages & Disadvantages of Digital Cheaper Less susceptible to noise Greater attenuation

Pulses become rounded and smaller Leads to loss of information


Amara 61

Attenuation of Digital Signals


Amara 62

Components of Speech Frequency range (of hearing) 20Hz-20kHz

Speech 100Hz-7kHz Easily converted into electromagnetic signal

for transmission Sound frequencies with varying volume

converted into electromagnetic frequencies with varying voltage

Limit frequency range for voice channel 300-3400Hz


Amara 63

Conversion of Voice Input into Analog Signal


Amara 64

Video Components USA - 483 lines scanned per frame at 30 frames per

second 525 lines but 42 lost during vertical retrace

So 525 lines x 30 scans = 15750 lines per second 63.5s per line 11s for retrace, so 52.5 s per video line

Max frequency if line alternates black and white Horizontal resolution is about 450 lines giving 225

cycles of wave in 52.5 s Max frequency of 4.2MHz


Amara 65

Binary Digital Data

From computer terminals etc. Two dc components Bandwidth depends on data rate


Amara 66

Conversion of PC Input to Digital Signal


Amara 67

Data and Signals

Usually use digital signals for digital data and analog signals for analog data

Can use analog signal to carry digital data Modem

Can use digital signal to carry analog data Compact Disc audio


Amara 68

Analog Signals Carrying Analog and Digital Data


Amara 69

Digital Signals Carrying Analog and Digital Data


Amara 70

Analog Transmission

Analog signal transmitted without regard to content

May be analog or digital data Attenuated over distance Use amplifiers to boost signal Also amplifies noise


Amara 71

Digital Transmission Concerned with content Integrity endangered by noise, attenuation

etc. Repeaters used Repeater receives signal Extracts bit pattern Retransmits Attenuation is overcome Noise is not amplified


Amara 72

Advantages of Digital Transmission Digital technology

Low cost LSI/VLSI technology Data integrity

Longer distances over lower quality lines Capacity utilization

High bandwidth links economical High degree of multiplexing easier with digital techniques

Security & Privacy Encryption

Integration Can treat analog and digital data similarly


Amara 73

Transmission Impairments Signal received may differ from signal

transmitted Analog - degradation of signal quality Digital - bit errors Caused by

Attenuation and attenuation distortion Delay distortion Noise


Amara 74

Attenuation Signal strength falls off with distance Depends on medium Received signal strength:

must be enough to be detected must be sufficiently higher than noise to be

received without error Attenuation is an increasing function of

frequency


Amara 75

Delay Distortion

Only in guided media Propagation velocity varies with frequency


Amara 76

Noise (1) Additional signals inserted between

transmitter and receiver Thermal

Due to thermal agitation of electrons Uniformly distributed White noise

Intermodulation Signals that are the sum and difference of original

frequencies sharing a medium


Amara 77

Noise (2) Crosstalk

A signal from one line is picked up by another Impulse

Irregular pulses or spikes e.g. External electromagnetic interference Short duration High amplitude


Amara 78

More on Thermal (White) Noise Power of thermal noise present in a

bandwidth B (Hz) is given by

T is absolute temperature in kelvin and k is Boltzmann’s constant k = 1.3810-23 J/K

0 (watts)

= 228.6 10log 10log (dBw)

N kTB N B

T B

= =

- + +


Amara 79

Channel Capacity Data rate

In bits per second Rate at which data can be communicated

Bandwidth In cycles per second of Hertz Constrained by transmitter and medium


Amara 80

Nyquist Bandwidth If rate of signal transmission is 2B then signal

with frequencies no greater than B is sufficient to carry signal rate

Given bandwidth B, highest signal rate is 2B Given binary signal, data rate supported by B

Hz is 2B bps Can be increased by using M signal levels C= 2B log2M


Amara 81

Shannon Capacity Formula Consider data rate,noise and error rate Faster data rate shortens each bit so burst of

noise affects more bits At given noise level, high data rate means higher

error rate Signal to noise ratio (in decibels) SNRdB

=10 log10 (signal/noise)

Capacity C=B log2(1+SNR) This is error free capacity


Amara 82

Eb/N0 Determines digital data rates and error rates Standard quality measure for digital

communication system performance Ratio of signal energy per bit to noise power

density per Hertz Eb = energy per bit in a signal (Joules) = STb,

where S = signal power (Watts), Tb = time required to send 1 bit (seconds) R = bit rate = 1/ Tb

0 0

/b bE ST S R S

N N kT kTR


Amara 83

Eb/N0 (Cont.)

Bit error rate for digital data is a decreasing function of Eb/N0

Given Eb/N0 to achieve a desired error rate, parameters in formula above may be selected

Eb/N0 does not depend on bandwidth (vs. SNR)

N = N0BT

0

10log 10log 10log

10 log 228.6 10log

bdBW

dB

dBW

ES R k T

N

S R dBW T

0 0

/b T TE B BS R SSNR

N N N R R


Amara 84

Eb/N0 (Cont.) Shannon’s result can be rewritten as:

Relates achievable spectral efficiency C/B to Eb/N0

0

0

2 1

Setting and in

2 1

C B

b TT

C Bb

SSNR

NE B

B B R C SNRN R

E B

N C

coe 342: data & computer communications (t042) dr. marwan abu-amara chapter 3: data transmission

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