COE 341: Data & Computer Communications (T061) Dr. Marwan Abu-Amara Chapter 5: Data Encoding.

COE 341: Data & Computer Communications (T061)Dr. Marwan Abu-Amara

Chapter 5:

Data Encoding

COE 341 (T061) – Dr. Marwan Abu-

Amara 2

Encoding and Modulation Techniques


Amara 3

Digital & Analog Signaling Digital signaling

Data source g(t) encoded into digital signal x(t) g(t) may be analog (e.g. voice) or digital (e.g. file) x(t) dependent on coding technique, chosen to

optimize use of transmission medium Conserve bandwidth or minimize errors

Analog signaling Based on continuous constant frequency signal,

carrier signal (i.e. A cos(2fct+) or A sin(2fct+)) Carrier signal frequency chosen to be compatible

with transmission medium Data transmitted by carrier signal modulation by

manipulating A, fc, and/or


Amara 4

Analog Signaling Modulation

Process of encoding source data onto a carrier signal with frequency fc

Operation on one or more of three fundamental frequency-domain parameters: amplitude, frequency, and phase

Input signal m(t) Can be analog or digital Called modulating signal or baseband signal Modulated signal s(t) is result of modulating carrier signal;

called bandlimited or bandpass signal Location of bandwidth on spectrum related to carrier

frequency fc


Amara 5

Baseband vs. Bandpass Signals Baseband Signal:

Spectrum not centered around non zero frequency May have a DC component

Bandpass Signal: Does not have a DC component Finite bandwidth around or at fc


Amara 6

Encoding and Modulation: Remarks Encoding is simpler and less expensive than modulation

Encoding into digital signals allows use of modern digital transmission and switching equipment Basis for Time Division Multiplexing (TDM)

Modulation shifts baseband signals to a different region of the frequency spectrum Basis for Frequency Division Multiplexing (FDM)

Unguided media and optical fibers can carry only analog signals


Amara 7

Encoding Techniques Digital data, digital signal

Simple and inexpensive equipment Analog data, digital signal

Data needs to be converted to digital form Digital data, analog signal

Take advantage of existing analog transmission media

Analog data, analog signal Transmitted as baseband signal easily and cheaply


Amara 8

Digital Data, Digital Signal Digital signal

Sequence of discrete, discontinuous voltage pulses Each pulse is a signal element Binary data encoded into signal elements

Unipolar signal All signal elements have same sign (e.g. 0: +5 V, 1:

+10 V DC content) Polar signal

One logic state represented by positive voltage & the other by negative voltage (e.g. 0: +5 V, 1: -5 V ideally Zero DC content)


Amara 9

Digital Data, Digital Signal … Mark and Space

Binary 1 and Binary 0 respectively

Duration or length of a bit (Tb) Time taken for transmitter to emit the bit

Data rate, R ( = 1/Tb) Rate of data transmission in bits per second (bps)

Duration of a Signal Element (Ts) Minimum signal pulse duration

Modulation (signaling) rate (1/Ts) Rate at which the signal level changes with time Measured in bauds = signal elements per second


Amara 10

Digital Data, Digital Signal …

Data rate = 1/1s

= 1 M bps

Signaling Rate for NRZI: = 1/1s

= 1 M bauds

Signaling Rate for Manchester: = 1/0.5s

= 2 M bauds

Tb

Ts

Ts


Amara 11

Interpretation of the Received Signal


Amara 12

Interpreting Digital Signal at Receiver Receiver need to know

Timing of bits - when they start and end Signal level Sampling & comparison with a threshold value

Factors affecting successful interpretation of signals: signal to noise ratio, data rate, bandwidth Increase in data rate increases bit-error-rate (BER) Increase in SNR decreases BER Increase in bandwidth allows for increase in data

rate


Amara 13

Comparison of Encoding Schemes Encoding scheme

Mapping from data bits to signal elements Signal Spectrum

Lack of high frequencies reduces required bandwidth Lack of dc component allows ac coupling via transformer

providing isolation & reducing interference Transfer function of a channel is worse near the band edges

Concentrate power in the middle of the bandwidth Clocking

Synchronizing transmitter and receiver Sync mechanism based on signal

can be built into signal encoding


Amara 14

Comparison of Encoding Schemes Error detection

Can be built into signal encoding Signal interference and noise immunity

Some codes are better than others Cost and complexity

Higher signal rate (& thus data rate) lead to higher costs

Some codes require signal rate greater than data rate


Amara 15

Encoding Schemes

Nonreturn to Zero-Level (NRZ-L) Nonreturn to Zero Inverted (NRZI) Bipolar –AMI (alternate mark inversion) Pseudoternary Manchester Differential Manchester


Amara 16

Nonreturn to Zero-Level (NRZ-L) Two different voltages for 0 and 1 bits Voltage constant during bit interval

no transition, no return to zero voltage e.g. Absence of voltage for zero, constant positive

voltage for one More often, negative voltage for one value (1) and

positive for the other (0) Used to generate or interpret digital data by

terminals An example of absolute encoding

Encoding data as a signal level


Amara 17

Nonreturn to Zero Inverted (NRZI) Nonreturn to zero inverted on ones Constant voltage pulse for duration of bit Data encoded as presence or absence of

signal transition at beginning of bit time Transition (low to high or high to low) denotes a

binary 1 No transition denotes binary 0

An example of differential encoding Info to be transmitted represented as changes

between successive signal elements


Amara 18

NRZ

Transition Denotes

one

(+)ve

(–)ve


Amara 19

NRZ pros and cons

Pros Easy to engineer Make good use of bandwidth

Cons Large dc component Lack of synchronization capability

No signal transitions for long strings of 0’s or 1’s

Used for magnetic recording Not often used for signal transmission


Amara 20

Differential Encoding Data represented by signal transitions rather

than signal levels Advantages;

With noise, signal transitions are detected more easily than signal levels

In complex transmission layouts, it is easy to accidentally lose sense of polarity

+_

RXEffect of swapping terminals on:- NRZ-L - NRZI


Amara 21

NRZ pros and cons


Amara 22

Multilevel Binary Use more than two signaling levels Bipolar-AMI (Alternate Mark Inversion)

zero represented by no line signal one represented by positive or negative pulse one pulses alternate in polarity No loss of sync if a long string of ones (zeros still

a problem) No net dc component Lower bandwidth Easy error detection


Amara 23

Pseudoternary

One represented by absence of line signal Zero represented by alternating positive and

negative No advantage or disadvantage over bipolar-

AMI


Amara 24

Bipolar-AMI and Pseudoternary All Single Pulse Errors-

Detected

CancelingAdding

Double Pulse Error-Undetected

Double Pulse Error-Detected


Amara 25

Trade Off for Multilevel Binary Not as efficient as NRZ

Each signal element only represents one bit Date Rate=R=1/TB

In a 3 level system could represent log23 = 1.58 bits

Receiver must distinguish between three levels (+A, -A, 0)

Requires approximately 3dB more signal power for same probability of bit error


Amara 26

Theoretical Bit Error Rate for Various Encoding Schemes


Amara 27

Biphase Manchester

Transition in middle of each bit period Transition serves as clock and data High to low represents zero Low to high represents one Used by IEEE 802.3 (Standard for baseband coaxial cable

& twisted pair CSMA/CD bus LANs) Differential Manchester

Mid bit transition is clocking only Transition at start of a bit period represents zero No transition at start of a bit period represents one Note: this is a differential encoding scheme Used by IEEE 802.5 (Token ring LAN)


Amara 28

Manchester Encoding


Amara 29

Differential Manchester Encoding


Amara 30


Amara 31

Biphase Pros and Cons Pros

Synchronization on mid bit transition (self clocking) No dc component Error detection

Absence of expected transition

Con At least one transition per bit time and possibly two

Maximum modulation rate is twice NRZ Requires more bandwidth


Amara 32

Modulation (Signaling) Rate Data rate (R)

Bits per second, or bit rate 1/Tb, where Tb is bit duration

Modulation rate (D) Rate at which signal elements generated Measured in Baud Modulation Rate D = R × k

R = data rate in bps M = signaling levels used L = bits/signal element = log2 M k = signal elements per bit = signal trans./bit trans. = 1/L

In General, Modulation Rate D = R × k = R/log2 M


Amara 33

Tb

Ts

Ts

k=1

k=2

Modulation (Signaling) Rate …

So, for Manchester

D= kR = 2/Tb


Amara 34

Scrambling Use scrambling to replace sequences that would

produce constant voltage Filling sequence

Must produce enough transitions to sync Must be recognized by receiver and replace with original Same length as original Not be likely to be generated by noise

No dc component No long sequences of zero level line signal No reduction in data rate Error detection capability


Amara 35

B8ZS Bipolar With 8 Zeros Substitution Based on bipolar-AMI If octet of all zeros and last voltage pulse

preceding was positive encode as 000+-0-+ If octet of all zeros and last voltage pulse

preceding was negative encode as 000-+0+- Causes two violations of AMI code Unlikely to occur as a result of noise Receiver detects and interprets as octet of all

zeros


Amara 36

HDB3

High Density Bipolar 3 Zeros Based on bipolar-AMI String of four zeros replaced with one or two

pulses


Amara 37

B8ZS and HDB3

1s


Amara 38

Digital Data, Analog Signal Transmission of digital data through public

telephone network Public telephone system

300Hz to 3400Hz Use modem (modulator-demodulator)

Encoding techniques modify one of three characteristics of carrier signal Amplitude => Amplitude shift keying (ASK) Frequency => Frequency shift keying (FSK) Phase => Phase shift keying (PSK)

Resulting signal has a bandwidth centered on carrier frequency


Amara 39

Digital Data, Analog Signal


Amara 40

Amplitude Shift Keying (ASK)

Binary values represented by different amplitudes of carrier

Usually, one amplitude is zero i.e. presence and absence of carrier is used

For a carrier signal resulting signal is

)2cos()( tfAts c

cos(2 ) binary 1( )

0 binary 0cA f t

s t


Amara 41

Amplitude Shift Keying (ASK)

Inefficient: up to 1200bps on voice grade lines Used to transmit digital data over optical fiber


Amara 42

Frequency Shift Keying (FSK) Binary values represented by two different

frequencies near carrier frequency Resulting signal is

f1 and f2 are offset from carrier frequency fc by equal but opposite amounts

0binary )2cos(

1binary )2cos()(

2

1

tfA

tfAts

fcf1 f2

fc fc


Amara 43

Frequency Shift Keying (FSK)

Less susceptible to error than ASK Up to 1200bps on voice grade lines Used for high frequency (3 to 30 MHz) radio

transmission Even higher frequencies on LANs using coaxial

cables


Amara 44

FSK

f1

Carrier 2

Datasignal

Carrier 1

vd(t)

v1(t), f1

v2(t), f2

vFSK(t)

Signalpower

Frequency

frequency spectrum

f2fcf f


Amara 45

Frequency Shift Keying (FSK) Full-duplex transmission over voice grade line

In one direction fc is 1170 Hz with f1 and f2 given by 1170+100=1270 Hz and 1170–100=1070 Hz

In other direction fc is 2125 Hz with f1 and f2 given by 2125+100=2225 Hz and 2125–100=2025 Hz


Amara 46

Phase Shift Keying (PSK) Binary PSK: Phase of carrier signal is shifted to

represent different values Phase shift of 180o

Differential PSK: Two-phase system with differential PSK Phase shift relative to previous bit transmitted rather

than some constant reference signal Binary 0 represented by sending a signal burst of

same phase as previous signal burst Binary 1 represented by sending a signal burst of

opposite phase as previous signal burst

cos(2 ) binary 0( )

cos(2 ) binary 1c

c

A f ts t

A f t


Amara 47

BPSK


Amara 48

Differential PSK (DPSK) Phase shifted relative to previous signal element

rather than some reference signal:

1: Reverse phase 0: Do not reverse phase (A form of differential encoding) Advantage: - No need for a reference oscillator at RX to determine absolute phase


Amara 49

Quadrature PSK (QPSK) More efficient Bandwidth use by each signal element

representing more than one bit Shifts of /2 (90o) Resulting signal is

Each signal element represents two bits

01binary )4

72cos(

00binary )4

52cos(

10binary )4

32cos(

11binary )4

2cos(

)(

tfA

tfA

tfA

tfA

ts

c

c

c

c


Amara 50

Quadrature PSK (QPSK)


Amara 51

Quadrature Amplitude Modulation (QAM) An extension of the QPSK just described

Combines both ASK and PSK For example, ASK with 2 levels and

PSK with 4 levels give 4 x 2 i.e. 8-QAM Up to M=256 is possible Large bandwidth savings But some susceptibility to

noise QAM used on asymmetric

digital subscriber line

(ADSL) and some wireless

systems

Constellation

M=8, L = 3


Amara 52

Multilevel PSK (MPSK) Can use more phase angles and even

have more than one amplitude! For example, 9600 bps modems use

12 phase angles, four of which have 2 amplitudes

Gives 16 different signal elements M = 16 and L = log2 (16) = 4 bits

Every signal element carries 4 bits (Data sent 4 bits at a time)

Baud rate is only 9600/4 = 2400 bauds (OK for a voice grade line)

Complex signal encoding allows high data rates to be sent on voice grade lines having a limited bandwidth


Amara 53

Data Rate & Modulation Rate In general

D: modulation rate (signals per second or bauds) R: data rate (bits per second) M: number of different signal elements L: number of bits per signal element

With line signaling speed of 2400 baud For NRZ-L, data rate is 1/Tb

For PSK, using L=16 different combinations of amplitude and phase, data rate is 9600 bps, R = 4/Tb

For bi-phase, Data rate is 2/Tb

2log

4 16 and 9600

R RD

L M

for L M R


Amara 54

Performance of D/A Modulation Schemes Performance of digital-to-analog techniques depends on the

definition of the bandwidth of the modulated signal Bandwidth of modulated signal depends on factors such as

Filtering technique used to create the band-pass signal ASK and PSK bandwidth directly related to bit rate Transmission bandwidth BT for ASK and PSK is

R is data rate r is related to filtering technique; 0< r <1

Transmission bandwidth BT for FSK is

where the delta for offset from the carrier frequency:

RrBT )1(

RrFBT )1(2

2 2 11c cF f f f f ff


Amara 55

Performance of D/A Modulation Schemes With multilevel signaling, bandwidth can

improve significantly

In the presence of noise, bit error rate of PSK and QPSK are about 3dB superior to ASK and FSK (as shown in Figure 5.4)

2

2

1 1MPSK:

log

1MFSK:

log

T

T

r rB R R

L M

r MB R

M


Amara 56

Bandwidth Efficiency Bandwidth efficiency is the ratio of data rate

to transmission bandwidth, R/BT

r = 0 r = 0.5 r = 1

ASK 1.0 0.67 0.5

FSK (wideband F >> R) 0 0 0

FSK (narrowband F fc) 1.0 0.67 0.5

PSK 1.0 0.67 0.5

MPSK: M=4, L=2 2.0 1.33 1.0

MPSK: M=8, L=3 3.0 2.00 1.5

MPSK: M=16, L=4 4.0 2.67 2.0

MPSK: M=32, L=5 5.0 3.33 2.5


Amara 57

Bandwidth Efficiency & Bit Error Rate The bit error rate (BER) can be reduced by increasing Eb/N0

Bit error rate can be reduced by decreasing bandwidth efficiency Increasing bandwidth Decreasing data rate N0 is the noise power density in watts/hertz. Hence,

the noise in a signal with bandwidth BT,, N=N0 BT


Amara 58

Bandwidth Efficiency & Bit Error Rate

For multi-level signaling, replace R with D

0 0

0

0 0

1

( )

b T

T

T

bdB

T dBdB

b

efficiency

E BS S S SNRRN N R N R N R BB

E RSNR

N B

E S S

N N R N B


Amara 59

Example What is the bandwidth efficiency for FSK, ASK,

PSK, and QPSK for a bit error rate of 10-7 on a channel with an SNR of 12dB ?

Recall that Bandwidth efficiency is the ratio of R/BT

0

0

12

bdB

T dBdB

b

T dBdB

E RSNR

N B

E RdB

N B


Amara 60

Example …

For FSK & ASK, Eb/N0 = 14.2dB

(R/BT)dB = – 2.2 dB, R/BT = 0.6 For PSK, Eb/N0 = 11.2dB

(R/BT)dB = 0.8 dB, R/BT = 1.2 For QPSK, D=R/2 (biphase) R/BT = 2.4


Amara 61

Analog vs. Digital Signaling Bandwidth Req. For digital signaling, bandwidth requirement

is approximated to be

For NRZ, D = R

DrBT )1(5.0

rB

R

T

1

2


Amara 62

Analog Data, Digital Signal Digitization

Conversion of analog data into digital data Digital data can be transmitted using NRZ-L Digital data can be transmitted using code other than

NRZ-L Digital data can then be converted to analog signal

Analog to digital conversion done using a codec Pulse code modulation Delta modulation


Amara 63

Pulse Code Modulation (PCM) Sampling Theorem: If a signal is sampled at

regular intervals at a rate higher than twice the highest signal frequency, the samples contain all the information of the original signal

Signal maybe constructed from samples using a low- pass filter

Voice data limited to below 4000Hz Require 8000 sample per second Analog samples (Pulse Amplitude Modulation, PAM) Each sample assigned digital value


Amara 64

Quantization

PAM Sample

n = 4 bits 24 = 16 Quantization levels

Transmitted Serial Code representing the PAM Samples:

Levels are numbered 0 to 15

Each PAM sample is assigned the number of the nearest quantization level and its digital code is transmitted

Sampling rate: 2B

Analog signal is band-limited with bandwidth B

Quantization Error

Must finish sending the n bits of the code before the next sample is due!


Amara 65

Pulse Code Modulation (PCM) 4 bit system gives 16 levels Quantized

Quantizing error or noise Approximations mean it is impossible to recover original

exactly SNR for quantizing error is

For each additional bit used for quantizing, SNR increases by about 6 dB or a factor of 4

8 bit sample gives 256 levels Quality comparable with analog transmission 8000 samples per second of 8 bits each gives

(80008) = 64 kbps

dBndBSNR n 76.102.6 76.12log20 10


Amara 66

PCM Example Suppose that we want to code an analog signal

that has voltage levels 0-5v using 2-bit PCM Then, we divide the the voltage level in four

intervals such that the size of each interval is 5/4=1.25 0-1.25, 1.25-2.5, 2.5-3.75, 3.75-5

We choose the values to be in the middle of each interval Selected values are: 0.625, 1.875, 3.125, 4.375 This guarantees that the maximum quantization error

is ½*5/4=0.625 and quantization SNR = 6 x 2 + 1.76 = 13.76 dB


Amara 67

Nonlinear Encoding Absolute error for each sample is the same

regardless of signal level Lower amplitude values are relatively more

distorted Solution is to make quantization levels not

evenly spaced Greater number of quantization steps for

lower amplitudes and smaller number of steps for higher amplitudes

Reduces overall signal distortion


Amara 68

Effect of Nonlinear Coding


Amara 69

Companding Effect of nonlinear coding can also be reduced

by companding Compressing-expanding More gain to weak signals than to strong signals on

input Reverse operation at output


Amara 70

Example (Problem 5-20) Consider an audio signal with spectral

components in the range of 300 to 3000 Hz. Assuming a sampling rate of 7000 samples per second will be used to generate the PCM signal. For SNR = 30 dB, what is the number of uniform

quantization levels needed? (SNR)dB = 6.02 n + 1.76 = 30 dB

n = (30 – 1.76)/6.02 = 4.69

Rounded off, n = 5 bits 25 = 32 quantization levels

What data rate is required? R = 7000 samples/sec 5 bits/sample = 35 Kbps


Amara 71

Delta Modulation Analog input is approximated by a staircase

function Move up or down one level () at each sample

interval Binary behavior

Function moves up or down at each sample interval A bit stream produced approximates derivative

of analog signal rather than its amplitude Produce a 1 if stair function is to go up Produce a 0 if stair function is to go down


Amara 72

Delta Modulation - example


Amara 73

Delta Modulation - Operation Analog input compared to most recent value of

approximating staircase function If value exceeds staircase function, generate a 1 Otherwise generate a 0

Output of DM process is a binary sequence to be used for reconstructing staircase function Reconstructed stair function is smoothed by a low

pass filter to reconstruct approximated analog signal


Amara 74

Delta Modulation - Operation


Amara 75

Delta Modulation Two important parameters in DM scheme

Size of step assigned to each binary digit Must be chosen to produce a balance between two types of

errors or noise If waveform changes slowly, quantizing noise increases with increase

in If waveform changes rapidly, slope overload noise increases with

decrease in Increasing sampling rate

improves the accuracy of the scheme Increases data rate

Principal advantage of DM is implementation simplicity PCM has better SNR at same data rate


Amara 76

CODEC - Performance Good voice reproduction

PCM - 128 levels (7 bit) Voice bandwidth 4 KHZ Data rate should be 8000 x 7 = 56 kbps for PCM

Bandwidth requirement Digital transmission requires 56 kbps for 4 KHz

analog signal Using Nyquist theorem, this signal requires in the

order of 28 KHz of Bandwidth, (C/2=56/2)


Amara 77

CODEC - Performance A common PCM scheme for color TV uses 10-

bit codes For bandwidth=4.6 MHz 92 Mbps (i.e. 2*4.6*10)

Digital techniques continue to grow in popularity Repeaters used with no additive noise Time-division multiplexing (TDM) is used for digital

signals with no intermodulation noise Use more efficient digital switching techniques

More efficient codes are used to reduce required bit rate


Amara 78

Analog Data, Analog Signals Modulation

Combining an input signal m(t) and a carrier at frequency fc to produce signal s(t) with bandwidth centered on fc

Why modulate analog signals? Higher frequency may be needed for effective transmission

For unguided transmission, impossible to send baseband signals as required antennas would be kilometers in diameter

Permits frequency division multiplexing Types of modulation

Amplitude Frequency Phase


Amara 79

Analog Modulation

Angle Modulation:(Phase, PM)

Angle Modulation: (Frequency, FM)

Amplitude Modulation (AM)

dt

df


Amara 80

Amplitude Modulation Simplest form of modulation Accos 2fct is the carrier, and x(t)= Amcos 2fmt is the input modulating signal Modulated signal expressed as:

na is the modulation index ( 1):

Added ‘1’ is a DC component to prevent loss of information – there will always be a carrier

Scheme is known as double sideband transmitted carrier (DSBTC)

tfAtfnts ccma 2cos]2cos1[)(

Amplitude of modulated wave

c

ma A

An

Portion of the modulating signal


Amara 81

Amplitude Modulation - Example Given the amplitude-modulating signal x(t)=Amcos 2fmt , find s(t):

Resulting signal has three components: At the original carrier frequency fc

A pair of additional components each

spaced fm Hz from the carrier Envelope of resulting signal is [1+na x(t)]

With na <1, envelope is exact reproduction of the modulating signal,So it can be recovered at receiver

With na >1, envelope crosses the time axis and information is lost

tffA

tffA

tfA

tffAn

tffAn

tfA

tftfnAts

mcm

mcm

cc

mcca

mcca

cc

cmac

)(2cos2

)(2cos2

2cos

)(2cos2

)(2cos2

2cos

2cos]2cos1[)(

c

ma A

An Am/2Am/2

Ac

fc fmfm


Amara 82

Amplitude Modulation - Examples

na = 0.5/1 = 0.5

MatLab Simulations

Envelope

ModulatingSignal

Carrier

ModulatedSignal

=(1+0.5cos2*pi*t)=(1+nacos2*pi*t)


Amara 83

Amplitude Modulation - Example

na = 1/1 = 1


Amara 84

Amplitude Modulation - Example

na = 2/1 = 2 (>1)


Amara 85

Spectrum of an AM signal: Modulating Signal havinga singleFrequency, fm

tffA

tffA

tfA

tffAn

tffAn

tfA

tftfnAts

mcm

mcm

cc

mcca

mcca

cc

cmac

)(2cos2

)(2cos2

2cos

)(2cos2

)(2cos2

2cos

2cos]2cos1[)(

Am/2Am/2

Ac

fc fmfm


Amara 86

Spectrum of an AM signal Spectrum of AM signal is original carrier plus spectrum of original

signal translated on both sides of fc Portion of spectrum f > fc is

upper sideband Portion of spectrum f < fc is

lower sideband Example: voice signal 300-3000Hz

With fc 60 KHz Upper sideband is 60.3-63 KHz Lower sideband is 57-59.7 KHz

Bandwidth Requirement: 2B

Modulating Signal havinga finiteBandwidth, B


Amara 87

Amplitude Modulation Total transmitted power Pt in modulated s(t) is given by

Pc is transmitted power in carrier na should be maximized (but <1) to allow most of signal power to

carry information Modulated signal contains redundant information

Only one of the sidebands is enough to restore modulating signal Possible ways to economize on transmitted power:

SSB: single sideband, eliminates one sideband and carrier, saves on BW (= B)

DSBSC: double sideband suppressed carrier, carrier is not transmitted, no saving on BW (= 2B)

Suppressing the carrier may not be OK in some applications, e.g. ASK, where the carrier can provide TX-RX synchronization.

21

2a

ct

nPP Am/2Am/2

Ac

fc fmfm


Amara 88

DSBSC: Double Sideband Suppressed Carrier - Example

Signal is expressed as tftxAts cc 2cos)]([)(

Suppressed Carrier


Amara 89

Angle Modulation Includes:

Frequency modulation (FM) and Phase modulation (PM) as special cases

Modulated signal is given by

Phase modulation (PM) Instantaneous Phase is proportional to modulating signal: np is phase modulation index

Frequency modulation (FM) Instantaneous frequency deviation is proportional to modulating

signal: i.e. Derivative of is proportional to modulating signal nf is frequency modulation index

)()( txnt p

)()( txnt f

)](2cos[)( ttfAts cc

Total Angle


Amara 90

Angle Modulation The total phase angle of s(t) at any instant is [2fct+(t)] Instantaneous phase deviation from carrier is (t) Phase Modulation (PM):

(t) = npx(t), instantaneous phase deviation from carrier is directly proportional to x(t)

Frequency Modulation (FM): Instantaneous angular frequency, , can be defined as the rate

of change of total phase So, for the modulated signal, s(t)

In FM, ’(t) is proportional to x(t). So, instantaneous frequency deviations from the carrier frequency is proportional to x(t).

)(2

1

)(2)(2)(2)(

tff

tfttfdt

dtft

ci

ccii

)(ti


Amara 91

Phase Modulation (PM)- Example Derive an expression for a phase-modulated signal s(t) with Ac= 5V, given the modulating signal

x(t) = 3 sin 2fmt We know that s(t):

For PM, (t) is given by:

Then s(t) is:

Instantaneous frequency of s(t) is:


)()( txnt p

]2sin32cos[5)( tfntfts mpc

tffnftffn

ftf mmpcmmp

ci

2cos32cos2

)2(3)(

Note: Frequency variations in s(t) lead x(t) amplitude variations by 90


Amara 92

Frequency Modulation: FM

Peak frequency deviation F is given by:

Where Am is the peak value of the modulating signal x(t)

An increase in the amplitude Am of x(t) increases F, which increases the bandwidth requirement BT

But average power level of the FM modulated signal is fixed at AC

2/2, (does not increase with Am)

In Amplitude Modulation, Am affects the power in the AM signal,

but does not affect the bandwidth

Hz 2

1mf AnF

)2sin()(

)()(

)(2

1

tfAtxand

txntand

tff

mm

f

ci


Amara 93

Frequency Modulation - Example Derive an expression for a frequency-modulated signal s(t) with Ac= 5V, given the modulating signal

x(t) = 3 sin 2fmt We know that s(t): For FM, ’(t) is given by:

Then s(t) is:

We have:

Substituting for F we get:


)()( txnt f

tff

ndttfndttt m

m

fmf

2cos

2

3 2sin3)()(

Hz 2

3fnF

]2cos2cos[5)( tff

Ftfts m

mc

But frequency varies as ’, i.e. as sin

not as – cos !!


Amara 94

Bandwidth Requirement

All AM, FM, and PM result in a modulated signal whose bandwidth is centered at fc

Let B be the bandwidth of the modulating signal For AM, BT = 2B Angle modulation includes a term of the form cos(…

+cos()) which is a nonlinear term producing a wide range of frequencies fc+fm, fc+2fm, … (the Bessel function)

i.e. Theoretically, an infinite bandwidth is required to transmit an FM or PM signal


Amara 95

Practical Bandwidth Requirement for Angle Modulation Carson’s Rule of thumb

For FM, BT= 2F + 2B Both FM and PM require greater bandwidth

than AM

BBT )1(2

FMfor 2B

F

PMfor

B

AnAn

mf

mp


Amara 96

Quadrature Amplitude Modulation (QAM) Popular analog signaling technique used in

asymmetric digital subscriber line (ADSL) Combination of amplitude and phase modulation Two signals transmitted simultaneously on same

carrier frequency using two copies of carrier one shifted by 90o

Each carrier is ASK modulated Input is a stream of binary digits arriving at a rate

of R bps Converted into two separate bits streams of R/2 bps


Amara 97

Quadrature Amplitude Modulation (QAM) One stream is ASK modulated on a carrier of

frequency fc

Other stream is ASK modulated on a carrier of frequency fc shifted by 90o

The two modulated signals are combined together and transmitted

Transmitted signal can be expressed astftdtftdts cc 2sin)(2cos)()( 21


Amara 98

QAM Modulator


Amara 99

Spread Spectrum Can be used to transmit analog or digital

data using analog signal Spread data over wide bandwidth Makes jamming and interception harder


Amara 100

Channel encoder receives input and converts it into analog signal with narrow bandwidth around center frequency

Signal is further modulated using a pseudorandom sequence

Modulation spreads the spectrum (increases bandwidth) of signal to be transmitted

Same pseudorandom sequence used to demodulate the spread spectrum signal

Spread Spectrum


Amara 101

Frequency hoping Spread Spectrum Signal broadcast over seemingly random

series of frequencies Hopping from one to another frequency in

split-second intervals Receiver also hops on the same frequencies

in synchronization with sender Difficult to catch and jam the signal without

knowing the frequencies


Amara 102


Amara 103

Direct Sequence Spread Spectrum Each bit is represented by multiple bits in

transmitted signal Multiple bits known as Chipping code Chipping code spreads signal across a wider

frequency band in direct proportion to number of bits used A 10-bit chipping code spreads signal across a

frequency band 10 times larger than 1-bit code Combine digital information stream with

pseudorandom bit stream using exclusive-OR


Amara 104

Direct Sequence Spread Spectrum


Amara 105

COE 341: Data & Computer Communications (T061) Dr. Marwan Abu-Amara Chapter 5: Data Encoding.

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