data and computer communications

Data and Computer Data and Computer CommunicationsCommunications

Eighth EditionEighth Edition

by William Stallingsby William Stallings

Lecture slides by Lawrie BrownLecture slides by Lawrie Brown

Chapter 5 – Signal Encoding Chapter 5 – Signal Encoding Techniques Techniques

Signal Encoding TechniquesSignal Encoding Techniques

Even the natives have difficulty mastering this peculiar vocabulary

—The Golden Bough, Sir James George Frazer

33

Encoding TechniquesEncoding Techniques

Digital dataDigital data

Analog dataAnalog data

• Digital Signal

• Analog Signal

• Digital Signal

• Analog Signal

Digital Data, Digital SignalDigital Data, Digital Signal

Digital signalDigital signal discrete, discontinuous voltage pulsesdiscrete, discontinuous voltage pulses each pulse is a signal elementeach pulse is a signal element binary data encoded into signal elementsbinary data encoded into signal elements


Modulation:Modulation: The process of encoding source data onto a carrier The process of encoding source data onto a carrier

signal with frequency signal with frequency ff

Carrier signalCarrier signal A continuous constant-frequency that is chosen to be A continuous constant-frequency that is chosen to be

compatible with the transmission media.compatible with the transmission media.

Baseband signal (modulating signal)Baseband signal (modulating signal) The input signal (analog or digital)The input signal (analog or digital)

The result of modulating the carrier signal is The result of modulating the carrier signal is called the modulated signal s(t)called the modulated signal s(t)

Some TermsSome Terms

UnipolarUnipolar All signal elements have the same sign.All signal elements have the same sign.

PolarPolar One logic state represented by positive voltage One logic state represented by positive voltage

the other by negative voltage.the other by negative voltage. data ratedata rate

Rate of data transmission in bits per secondRate of data transmission in bits per second

Some TermsSome Terms duration or length of a bitduration or length of a bit

Time taken for a transmitter to emit the bit Time taken for a transmitter to emit the bit (1/R)(1/R)

modulation ratemodulation rate Rate at which the signal level changes.Rate at which the signal level changes. Measured in baud = signal elements per Measured in baud = signal elements per

second.second. mark and spacemark and space

Binary 1 and Binary 0 respectiveBinary 1 and Binary 0 respectivelyly

Interpreting SignalsInterpreting Signals

need to knowneed to know timing of bits - when they start and endtiming of bits - when they start and end signal levelssignal levels

factors affecting signal interpretationfactors affecting signal interpretation signal to noise ratiosignal to noise ratio data ratedata rate bandwidthbandwidth encoding schemeencoding scheme

1010

Data Encoding CriteriaData Encoding Criteria

An An increaseincrease in DR in DR increasesincreases BER BER An An increaseincrease in SNR in SNR decreasesdecreases BER BER An An increaseincrease in BW allows an in BW allows an increaseincrease in in

DRDR The other factor that improves The other factor that improves

performance is the performance is the encoding schemeencoding scheme The encoding scheme is simply the The encoding scheme is simply the

mapping from data bits to signal elementsmapping from data bits to signal elements

1111

Encoding SchemesEncoding Schemes

Non-return to Zero-Level (NRZ-L)Non-return to Zero-Level (NRZ-L) Non-return to Zero Inverted (NRZI)Non-return to Zero Inverted (NRZI) Bipolar -AMIBipolar -AMI PseudoternaryPseudoternary ManchesterManchester Differential ManchesterDifferential Manchester B8ZSB8ZS HDB3HDB3

1212

Comparing Encoding Comparing Encoding SchemesSchemes

Signal spectrumSignal spectrum With lack of high-frequency components, less bandwidth With lack of high-frequency components, less bandwidth

requiredrequired With no DC component, AC coupling via transformer With no DC component, AC coupling via transformer

possiblepossible Concentrate power in the middle of the bandwidthConcentrate power in the middle of the bandwidth

ClockingClocking Ease of determining beginning and end of each bit Ease of determining beginning and end of each bit

positionposition Not easy task. Not easy task.

• Separate clock for synchronization .(expensive)Separate clock for synchronization .(expensive)• Synchronization based on the transmitted signalSynchronization based on the transmitted signal

1313

Comparing Encoding Comparing Encoding SchemesSchemes

Error detectionError detection Can be built into signal encodingCan be built into signal encoding

Signal interference and noise immunitySignal interference and noise immunity Performance in the presence of noisePerformance in the presence of noise

Cost and complexityCost and complexity The higher the signal rate to achieve a given data The higher the signal rate to achieve a given data

rate, the greater the costrate, the greater the cost Some codes require signal rate greater than data rateSome codes require signal rate greater than data rate

Encoding SchemesEncoding Schemes

Nonreturn to Zero-Level (NRZ-L)Nonreturn to Zero-Level (NRZ-L) two different voltages for 0 and 1 bitstwo different voltages for 0 and 1 bits voltage constant during bit intervalvoltage constant during bit interval

no transition I.e. no return to zero voltageno transition I.e. no return to zero voltage such as absence of voltage for zero, constant positive such as absence of voltage for zero, constant positive

voltage for onevoltage for one more often, negative voltage for one value and more often, negative voltage for one value and

positive for the otherpositive for the other

Nonreturn to Zero InvertedNonreturn to Zero Inverted nonreturn to zero inverted on onesnonreturn to zero inverted on ones constant voltage pulse for duration of bitconstant voltage pulse for duration of bit data encoded as presence or absence of signal transition at data encoded as presence or absence of signal transition at

beginning of bit timebeginning of bit time transition (low to high or high to low) denotes binary 1transition (low to high or high to low) denotes binary 1 no transition denotes binary 0no transition denotes binary 0

example of differential encoding since haveexample of differential encoding since have data represented by changes rather than levelsdata represented by changes rather than levels more reliable detection of transition rather than levelmore reliable detection of transition rather than level easy to lose sense of polarityeasy to lose sense of polarity

NRZ Pros & ConsNRZ Pros & Cons

ProsPros easy to engineereasy to engineer make good use of bandwidthmake good use of bandwidth

ConsCons dc componentdc component lack of synchronization capabilitylack of synchronization capability

used for magnetic recordingused for magnetic recording not often used for signal transmissionnot often used for signal transmission

Spectral Density of Various Signal Spectral Density of Various Signal Encoding SchemesEncoding Schemes

Most of the energy in NRZ and NRZI signals is between dc and half the bit rate. Most of the energy in NRZ and NRZI signals is between dc and half the bit rate. Data rate of 9600 bps, most of the energy in the signal is concentrated between dc and 4800 Hz.Data rate of 9600 bps, most of the energy in the signal is concentrated between dc and 4800 Hz.

1919

RZ encodingRZ encoding

Multilevel Binary Bipolar-AMIMultilevel Binary Bipolar-AMI Use more than two levelsUse more than two levels Bipolar-AMIBipolar-AMI

zero represented by no line signalzero represented by no line signal one represented by positive or negative pulseone represented by positive or negative pulse one pulses alternate in polarityone pulses alternate in polarity no loss of sync if a long string of onesno loss of sync if a long string of ones long runs of zeros still a problemlong runs of zeros still a problem no net dc componentno net dc component lower bandwidthlower bandwidth easy error detectioneasy error detection

Multilevel Binary Bipolar-AMIMultilevel Binary Bipolar-AMI

Multilevel BinaryMultilevel BinaryPseudoternaryPseudoternary

one represented by absence of line signalone represented by absence of line signal zero represented by alternating positive zero represented by alternating positive

and negativeand negative no advantage or disadvantage over no advantage or disadvantage over

bipolar-AMIbipolar-AMI each used in some applicationseach used in some applications

Multilevel BinaryMultilevel BinaryPseudoternaryPseudoternary

Multilevel Binary IssuesMultilevel Binary Issues

synchronization with long runs of 0’s or 1’ssynchronization with long runs of 0’s or 1’s can insert additional bits, cf ISDNcan insert additional bits, cf ISDN scramble data (later)scramble data (later)

not as efficient as NRZnot as efficient as NRZ each signal element only represents one biteach signal element only represents one bit

• receiver distinguishes between three levels: +A, -A, 0receiver distinguishes between three levels: +A, -A, 0

a 3 level system could represent loga 3 level system could represent log223 = 1.58 bits3 = 1.58 bits requires approx. 3dB more signal power for same requires approx. 3dB more signal power for same

probability of bit errorprobability of bit error

Theoretical Bit Error Rate for Theoretical Bit Error Rate for Various EncodingVarious Encoding

Manchester EncodingManchester Encoding has transition in middle of each bit periodhas transition in middle of each bit period transition serves as clock and datatransition serves as clock and data low to high represents onelow to high represents one high to low represents zerohigh to low represents zero used by IEEE 802.3used by IEEE 802.3

Differential Manchester Differential Manchester EncodingEncoding

midbit transition is clocking onlymidbit transition is clocking only transition at start of bit period representing 0transition at start of bit period representing 0 no transition at start of bit period representing 1no transition at start of bit period representing 1

this is a differential encoding schemethis is a differential encoding scheme used by IEEE 802.5 used by IEEE 802.5

Biphase Pros and ConsBiphase Pros and Cons ConCon

at least one transition per bit time and possibly twoat least one transition per bit time and possibly two maximum modulation rate is twice NRZmaximum modulation rate is twice NRZ requires more bandwidthrequires more bandwidth

ProsPros synchronization on mid bit transition (self clocking)synchronization on mid bit transition (self clocking) has no dc componenthas no dc component has error detectionhas error detection

• Absence of expected transitionAbsence of expected transition• Noise would have to invert both before and after expected Noise would have to invert both before and after expected

transition.transition.

Modulation RateModulation Rate

3030

Modulation/Baud RateModulation/Baud Rate

Baud rate, also known as signaling rate or modulation Baud rate, also known as signaling rate or modulation rate:rate: Signal elements per second (baud).Signal elements per second (baud). The rate at which signal elements are transmitted.The rate at which signal elements are transmitted. In general, In general, DD = = RR//LL = = RR/(/(loglog22 MM) )

• DD = modulation rate, baud = modulation rate, baud

• RR = data rate, bps = data rate, bps

• M M = number of different signal elements = 2= number of different signal elements = 2LL

• LL = number of bits per signal element = number of bits per signal element For two-level signaling (binary), For two-level signaling (binary),

bit rate is equal to the baud rate.bit rate is equal to the baud rate.

3131

Modulation/Baud RateModulation/Baud Rate

Example: a stream of binary ones at 1 Mbps.Example: a stream of binary ones at 1 Mbps.

NRZI is 1 MBaud.NRZI is 1 MBaud.

Manchester has 0.5 bits/signal element:Manchester has 0.5 bits/signal element:

Baud rate = Bit rateBaud rate = Bit rate//NNbb

= 1 Mbps/0.5= 1 Mbps/0.5

= 2 MBaud= 2 MBaud

3232

Signal element versus data elementSignal element versus data element

ScramblingScrambling use scrambling to replace sequences that would use scrambling to replace sequences that would

produce constant voltageproduce constant voltage these filling sequences mustthese filling sequences must

produce enough transitions to syncproduce enough transitions to sync be recognized by receiver & replaced with originalbe recognized by receiver & replaced with original be same length as originalbe same length as original

design goalsdesign goals have no dc componenthave no dc component have no long sequences of zero level line signalhave no long sequences of zero level line signal have no reduction in data ratehave no reduction in data rate give error detection capabilitygive error detection capability

3434

B8ZSB8ZS

Bipolar With 8 Zeros SubstitutionBipolar With 8 Zeros Substitution Based on bipolar-AMIBased on bipolar-AMI

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

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

Causes two violations of AMI codeCauses two violations of AMI code Unlikely to occur as a result of noiseUnlikely to occur as a result of noise

Receiver detects and interprets as octet of all Receiver detects and interprets as octet of all zeroszeros

3535

B8ZSB8ZS

V: violation voltage that breaks AMI rule of encoding (opposite polarity from the previous)B: Bipolar a nonzero level voltage in accordance with the AMI rule

3636

Scrambling TechniquesScrambling Techniques

HDB3:HDB3: High Density Bipolar 3 zeros.High Density Bipolar 3 zeros. String of four zeros replaced with one or two pulses.String of four zeros replaced with one or two pulses. 4 zeros are encoded as either 000-, 000+, +00+, or -00-4 zeros are encoded as either 000-, 000+, +00+, or -00- Number of the non-zero pulses after last substitution is odd Number of the non-zero pulses after last substitution is odd

use (000V)use (000V) Number of the non-zero pulses after last substitution is even Number of the non-zero pulses after last substitution is even

use (B00V)use (B00V) Substitution rule is s.t. the 4th bit is always a code violation, Substitution rule is s.t. the 4th bit is always a code violation,

and successive violations are of alternate polarity (not to and successive violations are of alternate polarity (not to introduce dc component)introduce dc component)

B8ZS and HDB3B8ZS and HDB3

Digital Data, Analog SignalDigital Data, Analog Signal

main use is public telephone systemmain use is public telephone system has freq range of 300Hz to 3400Hzhas freq range of 300Hz to 3400Hz use modem (modulator-demodulator)use modem (modulator-demodulator)

encoding techniquesencoding techniques Amplitude shift keying (ASK)Amplitude shift keying (ASK) Frequency shift keying (FSK)Frequency shift keying (FSK) Phase shift keying (PK)Phase shift keying (PK)

Modulation TechniquesModulation Techniques

Amplitude Shift KeyingAmplitude Shift Keying One binary digit represented by presence of One binary digit represented by presence of

carrier, at constant amplitudecarrier, at constant amplitude Other binary digit represented by absence of Other binary digit represented by absence of

carriercarrier

where the carrier signal is where the carrier signal is A A cos(2cos(2ππffcctt))

0binary 0

1binary )2cos()(

tfAts c

4141

ASK CharacteristicsASK Characteristics

Susceptible to sudden gain changesSusceptible to sudden gain changes Inefficient modulation techniqueInefficient modulation technique used forused for

On voice-grade lines, used up to 1200 bpsOn voice-grade lines, used up to 1200 bps Used to transmit digital data over optical fiberUsed to transmit digital data over optical fiber

4242

ASK ImplementationASK Implementation

4343

Amplitude Shift KeyingAmplitude Shift Keying

The carrier is only one simple sine wave, the process of modulation produce s a nonperiodic composite signal

4444

Binary Frequency-Shift Keying Binary Frequency-Shift Keying (BFSK)(BFSK)

Two binary digits represented by two different frequencies Two binary digits represented by two different frequencies near the carrier frequencynear the carrier frequency

where where ff11 and and ff22 are offset from carrier frequency are offset from carrier frequency ffcc by equal but by equal but

opposite amountsopposite amounts

ts tfA 12cos

tfA 22cos

1binary

0binary

4545

BFSK CharacteristicsBFSK Characteristics

Less susceptible to error than ASKLess susceptible to error than ASK On voice-grade lines, used up to 1200bpsOn voice-grade lines, used up to 1200bps Used for high-frequency (3 to 30 MHz) Used for high-frequency (3 to 30 MHz)

radio transmissionradio transmission Can be used at higher frequencies on Can be used at higher frequencies on

LANs that use coaxial cableLANs that use coaxial cable

4646

Relationship between baud rate and Relationship between baud rate and bandwidth in FSKbandwidth in FSK

4747

FSK on Voice Grade LineFSK on Voice Grade Line

Multiple FSKMultiple FSK

each signalling element represents more each signalling element represents more than one bitthan one bit

more than two frequencies usedmore than two frequencies used more bandwidth efficientmore bandwidth efficient more susceptible to errormore susceptible to error

4949


ffi i = = ffcc + (2i – 1 – + (2i – 1 – MM) ) ffdd

ffcc = the carrier frequency = the carrier frequency ffdd = the difference frequency = the difference frequency M = number of different signal element = 2M = number of different signal element = 2LL

L = number of bits per signal elementL = number of bits per signal element

Mi1 ,2cos)( tfAts ii

5050


To mach the data rate of the input, each signal element is To mach the data rate of the input, each signal element is hold for a period of Thold for a period of Tss = LT = LT T is a bit periodT is a bit period

One signal element encodes L bitsOne signal element encodes L bits

total bandwidth required = 2Mftotal bandwidth required = 2Mfdd

minimum frequency separation = 2fminimum frequency separation = 2fdd = 1/T = 1/Tss

modulator requires a bandwidth of Wmodulator requires a bandwidth of Wdd = 2Mf = 2Mfdd = M/T = M/Tss

Phase Shift KeyingPhase Shift Keying phase of carrier signal is shifted to represent dataphase of carrier signal is shifted to represent data binary PSKbinary PSK

two phases represent two binary digitstwo phases represent two binary digits

0binary )2cos(

1binary )2cos(

)2cos(

)2cos()(

tfA

tfA

tfA

tfAts

c

c

c

c

Phase Shift KeyingPhase Shift Keying

we define we define d(t) as the d(t) as the discrete function discrete function takes on the value of +1 for one bit time if takes on the value of +1 for one bit time if

the corresponding bit in the bit stream is 1 the corresponding bit in the bit stream is 1 the value -1 of for one bit time if the the value -1 of for one bit time if the

corresponding bit in the bit stream is 0corresponding bit in the bit stream is 0

)2cos()()( tftAdts cd

Phase Shift KeyingPhase Shift Keying differential PSKdifferential PSK

phase shifted relative to previous transmission phase shifted relative to previous transmission rather than some reference signalrather than some reference signal

Quadrature PSKQuadrature PSK

get more efficient use if each signal get more efficient use if each signal element represents more than one bitelement represents more than one bit eg. shifts of eg. shifts of /2 (90/2 (90oo)) each element represents two bitseach element represents two bits split input data stream in two & modulate onto split input data stream in two & modulate onto

carrier & phase shifted carriercarrier & phase shifted carrier can use 8 phase angles & more than one can use 8 phase angles & more than one

amplitudeamplitude 9600bps modem uses 12 angles, four of 9600bps modem uses 12 angles, four of

which have two amplitudeswhich have two amplitudes

5757


10 )4

2cos(

00 )4

32cos(

01 )4

32cos(

11 )4

2cos(

)(

tfA

tfA

tfA

tfA

ts

c

c

c

c

tftQtftIts cc 2sin)(2

12cos)(

2

1)(

5858


QPSK and OQPSK QPSK and OQPSK ModulatorsModulators

6060


Performance of Digital to Performance of Digital to Analog Modulation SchemesAnalog Modulation Schemes

BandwidthBandwidth depends on a variety of factorsdepends on a variety of factors

• including the definition of bandwidth used including the definition of bandwidth used • The filtering technique used to create the bandpass signalThe filtering technique used to create the bandpass signal

ASK/PSK bandwidth directly relates to bit rateASK/PSK bandwidth directly relates to bit rate

R = bit rateR = bit rate

r = related to techniques by which the signal is filtered. (0 < r r = related to techniques by which the signal is filtered. (0 < r < 1)< 1)

FSKFSK

RrBT )1(

RrFBT )1(2


for MFSK & MPSK have tradeoff between for MFSK & MPSK have tradeoff between bandwidth efficiency and error performancebandwidth efficiency and error performance

MPSKMPSK

MFSKMFSK RM

MrBT

2log

)1(

RM

rR

L

rBT

2log

11


in presence of noise:in presence of noise: bit error rate of PSK and QPSK are about 3dB bit error rate of PSK and QPSK are about 3dB

superior to ASK and FSKsuperior to ASK and FSK for MFSK & MPSK have tradeoff between for MFSK & MPSK have tradeoff between

bandwidth efficiency and error performance bandwidth efficiency and error performance

Quadrature Amplitude Quadrature Amplitude ModulationModulation

QAM used on asymmetric digital subscriber line QAM used on asymmetric digital subscriber line (ADSL) and some wireless(ADSL) and some wireless

combination of ASK and PSKcombination of ASK and PSK logical extension of QPSKlogical extension of QPSK send two different signals simultaneously on send two different signals simultaneously on

same carrier frequencysame carrier frequency use two copies of carrier, one shifted 90use two copies of carrier, one shifted 90°°

each carrier is ASK modulatedeach carrier is ASK modulated two independent signals over same mediumtwo independent signals over same medium demodulate and combine for original binary outputdemodulate and combine for original binary output

QAM ModulatorQAM Modulator

tftdtftdts cc 2sin)(2cos)()( 21

QAM VariantsQAM Variants

two level ASKtwo level ASK each of two streams in one of two stateseach of two streams in one of two states four state systemfour state system essentially QPSKessentially QPSK

four level ASKfour level ASK combined stream in one of 16 statescombined stream in one of 16 states

have 64 and 256 state systems have 64 and 256 state systems improved data rate for given bandwidthimproved data rate for given bandwidth

but increased potential error ratebut increased potential error rate

QAMQAM

Analog Data, Digital SignalAnalog Data, Digital Signal

digitization is conversion of analog data digitization is conversion of analog data into digital data which can then:into digital data which can then: be transmitted using NRZ-Lbe transmitted using NRZ-L be transmitted using code other than NRZ-Lbe transmitted using code other than NRZ-L be converted to analog signalbe converted to analog signal

analog to digital conversion done using a analog to digital conversion done using a codeccodec pulse code modulationpulse code modulation delta modulationdelta modulation

Digitizing Analog DataDigitizing Analog Data

Pulse Code Modulation (PCM)Pulse Code Modulation (PCM)

sampling theorem:sampling theorem: ““If a signal is sampled at regular intervals at a If a signal is sampled at regular intervals at a

rate higher than twice the highest signal rate higher than twice the highest signal frequency, the samples contain all information frequency, the samples contain all information in original signal”in original signal”

eg. 4000Hz voice data, requires 8000 sample eg. 4000Hz voice data, requires 8000 sample per secper sec

strictly have analog samples strictly have analog samples Pulse Amplitude Modulation (PAM)Pulse Amplitude Modulation (PAM)

so assign each a digital valueso assign each a digital value

PCM ExamplePCM Example

PCM Block DiagramPCM Block Diagram

7474

Quantization ErrorQuantization Error

Samples are quantized:Samples are quantized:– – Approximations mean it is impossible to Approximations mean it is impossible to recover original exactly.recover original exactly.– – Quantizing error or noise.Quantizing error or noise.– – nn-bit encoding, there are 2-bit encoding, there are 2nn levels:levels:

LL number of levels number of levels The error for any sample The error for any sample

-∆/2 ≤ error ≤ ∆/2 -∆/2 ≤ error ≤ ∆/2

L

VV maxmin

Quantization ErrorQuantization Error The contribution of the quantization error to the The contribution of the quantization error to the

SNRSNRdBdB of a signal depends on L or bits per of a signal depends on L or bits per sample nsample n

SNR = 20 log2SNR = 20 log2n n +1.76 dB = 6.02 n + 1.76 dB+1.76 dB = 6.02 n + 1.76 dB ≈ ≈ 66n n dB.dB.

each additional bit used for quantizing each additional bit used for quantizing increases SNR by about 6 dB, which is a increases SNR by about 6 dB, which is a factor of 4.factor of 4.

Non-Linear CodingNon-Linear Coding

CompandingCompanding The same effect can be achieved by using uniform The same effect can be achieved by using uniform

quantizing but companding (compressing-quantizing but companding (compressing-expanding) the input analog signalexpanding) the input analog signal

CompandingCompanding compresses the intensity range of a signal by imparting compresses the intensity range of a signal by imparting

more gain to weak signals than to strong signals on inputmore gain to weak signals than to strong signals on input

At output, the reverse operation is performedAt output, the reverse operation is performed

CompandingCompanding

Delta ModulationDelta Modulation analog input is approximated by a staircase analog input is approximated by a staircase

functionfunction can move up or down one level (can move up or down one level () at each sample ) at each sample

intervalinterval

has binary behaviorhas binary behavior since function only moves up or down at each sample since function only moves up or down at each sample

intervalinterval hence can encode each sample as single bithence can encode each sample as single bit 1 for up or 0 for down1 for up or 0 for down

Delta ModulationDelta Modulation

must be chosen to produce a balance must be chosen to produce a balance between two types of errors or noise.between two types of errors or noise.

When the analog waveform is changing When the analog waveform is changing very slowly, there will be quantizing noise. very slowly, there will be quantizing noise. This noise increases as This noise increases as is increased. is increased.

when the analog waveform is changing when the analog waveform is changing more rapidly than the staircase can follow, more rapidly than the staircase can follow, there is slope overload noisethere is slope overload noise

Delta Modulation ExampleDelta Modulation Example

Delta Modulation OperationDelta Modulation Operation

PCM verses Delta ModulationPCM verses Delta Modulation DM has simplicity compared to PCMDM has simplicity compared to PCM but has worse SNRbut has worse SNR issue of bandwidth usedissue of bandwidth used

eg. for good voice reproduction with PCMeg. for good voice reproduction with PCM• want 128 levels (7 bit) & voice bandwidth 4khzwant 128 levels (7 bit) & voice bandwidth 4khz• need 8000 x 7 = 56kbpsneed 8000 x 7 = 56kbps

data compression can improve on thisdata compression can improve on this still growing demand for digital signalsstill growing demand for digital signals

use of repeaters, TDM, efficient switchinguse of repeaters, TDM, efficient switching PCM preferred to DM for analog signalsPCM preferred to DM for analog signals

Analog Data, Analog SignalsAnalog Data, Analog Signals

Modulation: combine an input signal Modulation: combine an input signal mm((tt)) with a carrier with a carrier ffcc to produce a signal to produce a signal ss((tt).).

modulate carrier frequency with analog datamodulate carrier frequency with analog data why modulate analog signals?why modulate analog signals?

higher frequency can give more efficient transmissionhigher frequency can give more efficient transmission permits frequency division multiplexing (chapter 8)permits frequency division multiplexing (chapter 8)

types of modulationtypes of modulation AmplitudeAmplitude FrequencyFrequency PhasePhase

Analog Analog ModulationModulationTechniquesTechniques

Amplitude ModulationAmplitude Modulation Frequency ModulationFrequency Modulation Phase ModulationPhase Modulation

DSBTCDSBTC

AM is the simplest form of modulationAM is the simplest form of modulation

x(t) : the input signalx(t) : the input signal nnaa : known as the : known as the modulation indexmodulation index

the ratio of the amplitude of the input signal to the ratio of the amplitude of the input signal to the carrierthe carrier

tftxnts ca 2cos)](1[)(

ExampleExample

DSBTCDSBTC

The envelope of the resulting signal is [ 1 + nThe envelope of the resulting signal is [ 1 + naa x(t) ] x(t) ]

If nIf naa < 1, the envelope is an exact reproduction of < 1, the envelope is an exact reproduction of

the original signalthe original signal If nIf naa > 1, the envelope will cross the time axis and > 1, the envelope will cross the time axis and

information is lostinformation is lost

9090

Envelopes for various values of Envelopes for various values of mm

9191

Over ModulationOver Modulation

DSBTC SpectrumDSBTC Spectrum The spectrum consists of the original carrier plus The spectrum consists of the original carrier plus

the spectrum of the input signal translated tothe spectrum of the input signal translated to nna a should be as large as possible should be as large as possible

most of the signal power is used to carry informationmost of the signal power is used to carry information

2

2

1 an

cP

tP

9393

SSBSSB

SSB take advantage of the fact that each SSB take advantage of the fact that each side band contains all the transmitted side band contains all the transmitted informationinformation

BW is half, BBW is half, BTT = B = B

Less power is required, (no transmission of Less power is required, (no transmission of the other side band)the other side band)

9494

Angle ModulationAngle Modulation FM and PM are special cases of angle FM and PM are special cases of angle

modulationmodulation

For phase modulationFor phase modulation PM PM

For frequency modulation, the derivative of the For frequency modulation, the derivative of the phase is proportional to the modulating signalphase is proportional to the modulating signal

FMFM

)]([2cos )( c ttfAts c

)()( tmnt p

)()(' tmnt f

9595

Angle modulationAngle modulation

In PM the instantaneous phase deviation is In PM the instantaneous phase deviation is proportional to m(t)proportional to m(t)

For FMFor FM Frequency can be defined as the rate of change of Frequency can be defined as the rate of change of

phase of a signal, the inst. Frequency of s(t) is phase of a signal, the inst. Frequency of s(t) is

)(2

1)(

)](2[)(2

' tftf

ttfdt

dtf

ci

ci

9696

Angle modulationAngle modulation The peak deviation in FM can be seen to beThe peak deviation in FM can be seen to be

an increase in the magnitude of an increase in the magnitude of m(t) m(t) will increase will increase delta Fdelta F should increase the transmitted bandwidthshould increase the transmitted bandwidth

But will not increase the average power level of But will not increase the average power level of the FM signalthe FM signal

Compare with AMCompare with AM level of modulation affects the power in the AM signal level of modulation affects the power in the AM signal

but does not affect its bandwidth.but does not affect its bandwidth.

9797

Angle modulationAngle modulation

AM is linear process and produces frequencies AM is linear process and produces frequencies that are the sum and difference of the carrier that are the sum and difference of the carrier signal and the components of the modulating signal and the components of the modulating signalsignal

For AM For AM

Angle modulation is not linear which includes Angle modulation is not linear which includes cos(phi).cos(phi).

It may contain an infinite BWIt may contain an infinite BW

9898

Angle ModulationAngle Modulation

For practical, Carson’s ruleFor practical, Carson’s rule

For FMFor FM BFBT 22

FMforB

An

B

F

PMforAn

where

BB

mf

mp

T

2

)1(2

SummarySummary

looked at signal encoding techniqueslooked at signal encoding techniques digital data, digital signaldigital data, digital signal analog data, digital signalanalog data, digital signal digital data, analog signaldigital data, analog signal analog data, analog signalanalog data, analog signal

data and computer communications

Documents

signal elementbinary

signal interpretationsignal

transmitted signal

signal elementssignal

signal rate greater

absence of signal transition

signal level changes

data encoding criteriaan