Signals Signals and and

SpectraSpectra

CHAPTER CHAPTER 11

School of Computer and Communication School of Computer and Communication Engineering, Amir Razif Arief b. Jamil Engineering, Amir Razif Arief b. Jamil

AbdullahAbdullahEKT 431: Digital EKT 431: Digital Communications Communications

Lecture 1Lecture 1 222006-01-242006-01-24

Coursework ContributionCoursework ContributionCoursework:Coursework: Lab: 30%Lab: 30%

Project 1Project 1 Project 2Project 2 Project 3Project 3

Assignments, Attendance & Quizzes: 10%Assignments, Attendance & Quizzes: 10% Assignments; minimum 4.Assignments; minimum 4. Attendance; subjected to university regulation.Attendance; subjected to university regulation. Quizzes; minimum 8.Quizzes; minimum 8.

Test: 10 %Test: 10 % Two tests.Two tests.

Exam:Exam: 50% 50% Lecturer: Amir Razif Arief b. Jamil AbdullahLecturer: Amir Razif Arief b. Jamil Abdullah

Office: Grnd Floor, House #8A, KKF, Kuala PerlisOffice: Grnd Floor, House #8A, KKF, Kuala Perlis E-mail: amirrazif@unimap.edu.myE-mail: amirrazif@unimap.edu.my Office tel#: 04-9854251 @ 019 4659277Office tel#: 04-9854251 @ 019 4659277 HP#: Upon RequestHP#: Upon Request

Teaching Engineer: Mohd Fairuz b. Mohd FadzilTeaching Engineer: Mohd Fairuz b. Mohd Fadzil Office: House #1, KKF, Kuala PerlisOffice: House #1, KKF, Kuala Perlis

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Practical informationPractical information Course materialCourse material

Course text book: Course text book: ““Digital Communications: Fundamentals and Digital Communications: Fundamentals and

ApplicationsApplications” by Bernard Sklar,Prentice Hall, ” by Bernard Sklar,Prentice Hall, 2005, ISBN: 0-13-084788-72005, ISBN: 0-13-084788-7

Reference Books;Reference Books;““Introduction to Digital CommunicationsIntroduction to Digital Communications”, by ”, by

Pursley M.B, IE Pearson Hall 2005Pursley M.B, IE Pearson Hall 2005““Information Transmission, Modulation and Information Transmission, Modulation and

NoiseNoise”, by M.Schwartz, Mc Graw Hill 2005”, by M.Schwartz, Mc Graw Hill 2005““Digital CommunicationsDigital Communications”, by Proakis, John G. ”, by Proakis, John G.

International Eddition, Mc GrawHill 3International Eddition, Mc GrawHill 3rdrd Ed. Ed. 19951995

OutcomeOutcome• To understand and use various To understand and use various termterminologies in inologies in

Digital Communications.Digital Communications.

• To be able to explain the differences between To be able to explain the differences between analog and digital communications.analog and digital communications.

• To describe the basic building blocks of a digital To describe the basic building blocks of a digital communication system and the performance communication system and the performance objectives for good communication.objectives for good communication.

• To analyze the To analyze the signals transmissionsignals transmission via channel. via channel.

• To study the base band data To study the base band data transmissiontransmission, digital , digital modulationmodulation and and spread spectrumspread spectrum communications.communications.

• To explore the basic principles of To explore the basic principles of telephony telephony systemsystem..

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Today, we are going to talk Today, we are going to talk about:about:

What are the features of a digital communication What are the features of a digital communication system?system? Why “digital” instead of “analog”? Why “digital” instead of “analog”?

What do we need to know before taking off toward What do we need to know before taking off toward designing a DCS?designing a DCS? Classification of signalsClassification of signals Random processesRandom processes AutocorrelationAutocorrelation Power and energy spectral densitiesPower and energy spectral densities Noise in communication systemsNoise in communication systems Signal transmission through linear systemsSignal transmission through linear systems Bandwidth of a signalBandwidth of a signal

IntroductionIntroduction Deal with Deal with transformationtransformation of information; voice, of information; voice,

video or data, over a video or data, over a channelchannel that consists of wire, that consists of wire, waveguide and space.waveguide and space.

Digital communication systems are becoming Digital communication systems are becoming attractive attractive because of the growing because of the growing demanddemand for for data communication and digital transmission data communication and digital transmission offers offers data processing optionsdata processing options..

RevisionRevision• Signals & Systems

Fourier transform, signal analysis

• Communications Systems PAM, PWM, PPM, PCM, ASK, FSK, PSK, line

coding

• Communication NetworkLAN, wireless network, circuit switching,

multiple access

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Scope of the courseScope of the course• Communications is a process by which information Communications is a process by which information

is exchanged between individuals through a is exchanged between individuals through a common system of symbols, signs, or behaviour. common system of symbols, signs, or behaviour.

• Communication systems are reliable, economical Communication systems are reliable, economical and efficient means of communicationsand efficient means of communications• Public switched telephone network (PSTN), mobile Public switched telephone network (PSTN), mobile

telephone communication (GSM, 3G, ...), telephone communication (GSM, 3G, ...), broadcast radio or television, navigation systems, broadcast radio or television, navigation systems, ......

• The course is aiming at introducing fundamental The course is aiming at introducing fundamental issues in issues in designingdesigning a (digital) communication a (digital) communication systemsystem

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Scope of the course ...Scope of the course ...

• Example of a (digital) communication system: Example of a (digital) communication system: • Cellular wireless communication systemsCellular wireless communication systems

Base Station (BS)

User Equipment (UE)

UE UE

UE

BS

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Scope of the course …Scope of the course … Learning fundamental issues in designing a digital Learning fundamental issues in designing a digital

communication system (DCS):communication system (DCS): Utilized techniquesUtilized techniques

Formatting Formatting and source codingand source codingModulation (Baseband and bandpass signaling)Modulation (Baseband and bandpass signaling)Channel codingChannel codingEqualizationEqualizationSynchronizationSynchronization........

Design goalsDesign goals Trade-off between various parameters Trade-off between various parameters

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Block Diagram of DCSBlock Diagram of DCSGeneral structure of a communication General structure of a communication

systemsystem

FormatterSource encoder

Channel encoder

Modulator

FormatterSource decoder

Channel decoder

Demodulator

Transmitter

Receiver

SOURCEInfo.

Transmitter

Transmitted signal

Received signal

Receiver

Received info.

Noise

ChannelSource User

Block Diagram and Block Diagram and TransformationTransformation

• The upper block are the signal transformation from The upper block are the signal transformation from source to transmitter (XMT); source to transmitter (XMT); formatformat,, source encode source encode,, encryptencrypt,, channel encode channel encode,, multiplex multiplex,, pulse pulse modulatedmodulated,, band pass modulated band pass modulated,, frequency spread frequency spread and multiple excessand multiple excess..

• The lower block are the signal transformation from The lower block are the signal transformation from receiver (RCV) to sink; receiver (RCV) to sink; reversingreversing the signal the signal processing of the upper block.processing of the upper block.

• For wireless communication;For wireless communication;

(i) transmitter consist of frequency (i) transmitter consist of frequency up-up-conversionconversion stage to a radio frequency, stage to a radio frequency, high power high power amplifieramplifier and and antennaantenna..

(ii) receiver consist of antenna and low noise (ii) receiver consist of antenna and low noise amplifier (amplifier (LNALNA).).

• Signal processing steps;Signal processing steps;(i) input information source is convert to binary digits ((i) input information source is convert to binary digits (bitsbits) )

(ii) bits grouped to form (ii) bits grouped to form message symbolmessage symbol ((mmii ))(iii) system using channel coding; sequence of message (iii) system using channel coding; sequence of message symbol transform to sequence of symbol transform to sequence of channel symbolchannel symbol ((uuii ) or ) or bit streambit stream. .

• The key signal processing blocks of DCS are The key signal processing blocks of DCS are formattingformatting, , modulation,modulation, demodulation/detectiondemodulation/detection and and synchronizationsynchronization..(1)(1) FormattingFormatting: : transform source information into bits. Information is inform of transform source information into bits. Information is inform of bit bit streamstream up to pulse-modulation block. up to pulse-modulation block.

(2) Modulation(2) Modulation: : process of converting the channel symbol to waveform compatible to process of converting the channel symbol to waveform compatible to transmission channel.transmission channel.

- binary representation - binary representation baseband waveformbaseband waveform

Cont’d…Cont’d…

(3) Pulse Modulation(3) Pulse Modulation: : - - transform form binary representation to transform form binary representation to basebandbaseband waveform. waveform. Include filtering to minimize the binary waveform. When pulse Include filtering to minimize the binary waveform. When pulse modulation is applied to binary symbols result in modulation is applied to binary symbols result in pulse-code pulse-code modulationmodulation (PCM). (PCM). - line code, M-ary pulse modulation.- line code, M-ary pulse modulation.

(4)(4) Band Pass Modulation: Band Pass Modulation: - - required if the transmission medium do not support the propagation required if the transmission medium do not support the propagation of pulse-like waveform.of pulse-like waveform.

EqualizationEqualization- - implemented to implemented to compensatecompensate for any signal distortion caused by for any signal distortion caused by non-ideal non-ideal hhcc(t).(t).

Source CodinSource Codin- - produce AD conversion and remove redundant information.produce AD conversion and remove redundant information.- channel coding can reduce the probability of error and reduce snr.- channel coding can reduce the probability of error and reduce snr.

MultiplexingMultiplexing- combine signal of different characteristics or sources- combine signal of different characteristics or sources to share to share communication resources.communication resources.

EncryptionEncryption; ; - - provides communication privacy, prevent intrusion.provides communication privacy, prevent intrusion.

Cont’d…Cont’d…

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Digital Communication Digital Communication SystemSystem

Important features of a DCS:Important features of a DCS: The The transmitter transmitter sends a waveform from a finite sends a waveform from a finite

set of possible waveforms during a limited timeset of possible waveforms during a limited time

The The channelchannel distorts, attenuates the transmitted distorts, attenuates the transmitted signal and adds noise to it.signal and adds noise to it.

The The receiver receiver decides which waveform was decides which waveform was transmitted given the noisy received signaltransmitted given the noisy received signal

The probability of erroneous decision is an The probability of erroneous decision is an important measure for the system performanceimportant measure for the system performance

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Advantages Advantages of digital communications:of digital communications: Regenerator receiverRegenerator receiver Signal; original-> distortion-> degraded-> badly degraded.., -> Signal; original-> distortion-> degraded-> badly degraded.., ->

amplified & regeneratedamplified & regenerated

Different kinds of digital signal are treated Different kinds of digital signal are treated identically.identically.

Digital versus AnalogDigital versus Analog

DataVoice

Media

Propagation distance

Originalpulse

Regeneratedpulse

A bit is a bit!

Digital versus Analog ..cont’dDigital versus Analog ..cont’d

• Digital signals are Digital signals are regenerated.regenerated.• Less distortionLess distortion due to ‘1’ and ‘0’ state. due to ‘1’ and ‘0’ state.• Availability of Availability of error detectionerror detection and and correctioncorrection..• Digital is moreDigital is more reliable reliable, , cheapcheap cost and more cost and more flexibleflexible

compare to analog.compare to analog.• Different types of digital signals; data, telegraph, Different types of digital signals; data, telegraph,

telephone television, have identical signal telephone television, have identical signal transmissiontransmission a bita bit..

• Protect against Protect against interferenceinterference, , jammingjamming and provide and provide encryption/privacyencryption/privacy..

• Distorted analog signal cannot be removed by Distorted analog signal cannot be removed by amplification and cannot be regenerated.amplification and cannot be regenerated.

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Classification of SignalsClassification of Signals Deterministic and random signalsDeterministic and random signals

Deterministic signalDeterministic signal: No uncertainty with : No uncertainty with respect to the signal value at any time.respect to the signal value at any time.

Random signalRandom signal: Some degree of uncertainty in : Some degree of uncertainty in signal values before it actually occurs.signal values before it actually occurs.Thermal noise in electronic circuits due to the Thermal noise in electronic circuits due to the

random movement of electronsrandom movement of electronsReflection of radio waves from different Reflection of radio waves from different

layers of ionospherelayers of ionosphere

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Classification of Signals …Classification of Signals …

A discrete signal

Analog signals

A non-periodic signalA periodic signal

Periodic Periodic and and non-periodicnon-periodic signals signals

AnalogAnalog and and discrete discrete signalssignals

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Classification of Signals ..Classification of Signals .. Energy and power signalsEnergy and power signals

A signal is an A signal is an energy signalenergy signal if, and only if, it has if, and only if, it has nonzero but finite energy for all time:nonzero but finite energy for all time:

A signal is a A signal is a power signalpower signal if, and only if, it has if, and only if, it has finite but nonzero power for all time:finite but nonzero power for all time:

General rule: General rule: PeriodicPeriodic and and randomrandom signals are power signals are power signals.signals. Signals that are Signals that are both deterministic and both deterministic and non-periodic are energynon-periodic are energy signals. signals.

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Random ProcessRandom Process A random process is a collection of time functions, A random process is a collection of time functions,

or signals, corresponding to various outcomes of a or signals, corresponding to various outcomes of a random experiment. For each outcome, there random experiment. For each outcome, there exists a deterministic function, which is called a exists a deterministic function, which is called a sample function or a realization.sample function or a realization.

Sample functionsor realizations(deterministic

function)

Random variables

time (t)

Rea

l nu

mbe

r

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Random Process …Random Process … Strictly stationaryStrictly stationary: If none of the statistics of the : If none of the statistics of the

random process are affected by a shift in the time random process are affected by a shift in the time origin.origin.

Wide sense stationaryWide sense stationary (WSS): If the mean and (WSS): If the mean and autocorrelation functions do not change with a autocorrelation functions do not change with a shift in the origin time. shift in the origin time.

CyclostationaryCyclostationary: If the mean and autocorrelation : If the mean and autocorrelation functions are periodic in time.functions are periodic in time.

Ergodic processErgodic process: A random process is ergodic in : A random process is ergodic in mean and autocorrelation, if mean and autocorrelation, if

and, and, respectively.respectively.

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AutocorrelationAutocorrelation Defn: Defn: autocorrelation refers to the matching of a signal with autocorrelation refers to the matching of a signal with

a delayed version of itself.a delayed version of itself.

Autocorrelation of an Autocorrelation of an energy signalenergy signal

Autocorrelation of a Autocorrelation of a power signalpower signal

For a periodic signal:For a periodic signal:

Autocorrelation of a Autocorrelation of a random signalrandom signal

For a WSS process: For a WSS process:

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Spectral DensitySpectral Density• Energy signals:Energy signals:

• Energy spectral density (ESD): Energy spectral density (ESD):

• Power signals:Power signals:

• Power spectral density (PSD): Power spectral density (PSD):

• Random process:Random process:• Power spectral density (PSD): Power spectral density (PSD):

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Properties of an Properties of an Autocorrelation functionAutocorrelation function

For real-valued (and WSS in case of random For real-valued (and WSS in case of random signals):signals):

1.1. Autocorrelation and spectral density form a Autocorrelation and spectral density form a Fourier transform pair.Fourier transform pair.

2.2. Autocorrelation is symmetric around zero.Autocorrelation is symmetric around zero.

3.3. Its maximum value occurs at the origin.Its maximum value occurs at the origin.

4.4. Its value at the origin is equal to the average Its value at the origin is equal to the average power or energy.power or energy.

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Noise in Communication Noise in Communication SystemsSystems

• Thermal noise; Thermal noise; thermal motion of electrons in all thermal motion of electrons in all disipative componentsdisipative components,, is described by a zero-mean is described by a zero-mean Gaussian random process, n(t).Gaussian random process, n(t).

• Its PSD is flat, hence, it is called white noise.Its PSD is flat, hence, it is called white noise.• n- Gaussian probability density functionn- Gaussian probability density function

[w/Hz]

Probability density function

Power spectral density

Autocorrelation function

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Signal Transmission through Signal Transmission through Linear SystemsLinear Systems

Deterministic signals:Deterministic signals: Random signals:Random signals:

Ideal distortion less transmission:Ideal distortion less transmission: All the frequency components of the signal not only All the frequency components of the signal not only

arrive with an identical time delay, but also are arrive with an identical time delay, but also are amplified or attenuated equally. amplified or attenuated equally.

Input Output

Linear system

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Signal Transmission … - Signal Transmission … - cont’dcont’d

Ideal filters:Ideal filters:

Realizable filters:Realizable filters: RC filters Butterworth filterRC filters Butterworth filter

High-pass

Low-pass

Band-pass

Non-causal!

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Bandwidth of signalBandwidth of signal Baseband versus bandpass:Baseband versus bandpass:

Bandwidth dilemma:Bandwidth dilemma: Bandlimited signals are not realizable!Bandlimited signals are not realizable! Realizable signals have infinite bandwidth!Realizable signals have infinite bandwidth!

Baseband signal

Bandpass signal

Local oscillator

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Bandwidth of Signal …Bandwidth of Signal … Different definition of bandwidth:Different definition of bandwidth:

a) Half-power bandwidthb) Noise equivalent bandwidthc) Null-to-null bandwidth

a) Fractional power containment bandwidthb) Bounded power spectral densityc) Absolute bandwidth

(a)(b)

(c)(d)

(e)50dB