Analog & Digital Communications :

Asad AbbasAssistant Professor Telecom Department

Air University, E-9, Islamabad

Lec01_chapter01

2006-01-24 Lecture 1 2

Course Information Course text books:

Analog Communications Modern Digital and Analog Communication Systems

by B.P. Lathi

Digital Communications “Digital communications: Fundamentals and Applications”

by Bernard Sklar,Prentice Hall, 2001

Additional recommended books: “Communication systems engineering”, by John G.

Proakis and Masoud Salehi, Prentice Hall, 2002, 2nd edition, ISBN: 0-13-095007-6

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Scope of the course

Communication is a process by which information is exchanged between individuals through a common system of symbols, signs, or behavior

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

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

The course is aiming at introducing fundamental issues in designing analog and digital communication systems

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Scope of the course ... Example of a communication systems:

Cellular wireless communication systems

Base Station (BS)

User Equipment (UE)

UE UE

UE

BS

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Scope of the course ...

General structure of a communication systems

Analog Transmitter

Analog Receiver

SOURCEInfo.

Transmitter

Transmitted signal

Received signal

Receiver

Received info.

Noise

ChannelSource User

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Scope of the course ...

General structure of a communication systems

FormatterSource encoder

Channel encoder

Modulator

FormatterSource decoder

Channel decoder

Demodulator

Digital Transmitter

Digital Receiver

SOURCEInfo.

Transmitter

Transmitted signal

Received signal

Receiver

Received info.

Noise

ChannelSource User

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Review

Signal It is a set of information e.g. voice signal, video

signal etc

Signal Strength measurement Signal Energy Signal power

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Review

Signal Energy (real Signal)

Signal Energy (complex signal)

2 ( )gE g t dt

2( )gE g t dt

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Review

Signal Power ( Real Signal)

Signal Power (Complex Signal)

/ 221

/ 2

( )T

g TTT

P Lim g t dt

/ 221

/ 2

( )T

g TTT

P Lim g t dt

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Example

Power is infinite

Energy is infinite

Example 2

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Review

Classification of Signals Continuous Time and Discrete Time Signals Analog and Digital Signals Periodic and Aperiodic Signals Deterministic and Probabilistic Signals Energy and Power Signals

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Review

Classification of Signals Continuous –Time Signal

It is specified for every value of time of t

Discrete -Time Signal

It is specified for only at discrete values of t ( i.e. t=nT; n=1,2,3… )

2006-01-24 Lecture 1 14

Review…

Classification of Signals Analog Signal

A signal whose amplitude can take on any value in continuous range

Digital Signal Its amplitude can take on finite number of values The range set (dependent variable) contains

finite number of values. It may contain 2, 4, 8, 16, 32, 64, 128 or 256 values.

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Review…

Digital Signal Types.

Binary Signal (symbol/message) It is two valued digital signal. Each value is called bit or

some time symbol.

M-ary Signal (symbol/message) It is more than two values digital signal. Each value

represents two or more bits. Each value is called a symbol . The maximum number of

symbols (values) in M-ary signal are M. Each symbol consists of two or more bits. M=2, 4, 8, 16, 32, 64 ,……

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Review

M-ary Siginal .. The number bits per symbol are given by:

k = log2 M bits per symbol

Where M is total number of symbols.

If M=2, it is binary signal.

Periodic and non-periodic signals

x(t)=x(t+T) for all t

A non-periodic signalA periodic signal

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Review…

Deterministic and random signals Deterministic signal: No uncertainty with respect to

the signal value at any time.

Random signal: Some degree of uncertainty in signal values before it actually occurs.

Thermal noise in electronic circuits due to the random movement of electrons

Reflection of radio waves from different layers of ionosphere

The multipath signal in mobile communication system

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Review

Energy and power signals A signal is an energy signal if, and only if, it has nonzero but

finite energy for all time:

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

General rule: Periodic and random signals are power signals. Signals that are both deterministic and non-periodic are energy signals.

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Trigonometric Fourier Series

A periodic signal of period, To , consists of sum of sinusoids. The frequency of the fundamental term is 1/To The frequency of other terms, the harmonics, is integral

multiple of the fundamental (i.e. n/To; n=1, 2, 3..)

2

02

2

02

2

02

01

10

2

2

( ) cos sin

( )

( ) cos

( )sin

To

To

To

To

To

To

n o n on

T

n oT

n oT

x t a a n t b n t

a x t dt

a x t n t dt

b x t n t dt

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Example 2.22 ( B.P. Lathi)

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Example…

na

Spectrum of the signal (Plot of amplitudes vs frequency)All of the odd terms in F.S. expansion are zero, because the signal , w(t), is an even functionThe spectrum is discrete and its envelop is a sinc functionEven harmonics are zero because duty cycle is 50%

Importance of Fourier Series

It provides the details of frequency components which make up a periodic signal.

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Exponential Fourier Series

The periodic signal can also be represented in terms of exponentials as shown below.

2

02

1

( )

( )

o

To

oTo

jn tn

n

jn tn T

x t D e

D x t e dt

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Exponential Fourier Series of Example 2.22

Spectrum Comparison Trigonometric Fourier

Series Spectrum Spectrum is single sided

i.e., 0≤f<∞

Exponential Fourier Series Spectrum

Spectrum is double sided i.e.

-∞ <f<∞

22sin( )n

n na

12sin( )n

n nD

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Spectrum of A periodic Signal

The details of frequency components which make up an a periodic signal is given by its Fourier Transform

Fourier Transform of an aperiodic signal g(t) is given as:

The Inverse of Fourier Transform

2

212

( ) ( )

( ) ( )

( ) ( ) ( )

j t

j f t

j t j f t

G g t e dt

G f g t e dt

g t G e d G f e df

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Example

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Spectral Density

It is distribution of Signal’s energy or power in frequency domain.

Energy Spectral Density

The total Energy of a real valued energy signal x(t) is given by

Energy Spectral Density =

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Spectral Density (contd..)

Power Spectral Density of a Periodic Signal

The average power of a real valued deterministic power signal x(t) is given by: Parseval’s Theorem

2

2

02

02

2

2

22

0

2

0

2 2

0

1( )

1( )

1

To

To

T

o

T

To

To

x

jn tn

n

n

x n nn

P x t dtT

x t C e dtT

P C dt CT

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Note:Cn is same as Dn

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Spectral Density (contd..)

Power Spectral Density of Periodic Signal

= Power Spectral Density =

2( ) ; ... 3, 2, 1,0,1,2,3...

( )

n if

nn

x

P f C i

dPG f

df

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Spectral Density (contd..)

The Power Spectral density of a non-periodic power signal ( e.g. noise) is given by:

Where XT(f) is Fourier Transform xT(t), which is truncated version of x(t). It is observed in (-T/2, T/2)

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Example

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Example (contd..)

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Autocorrelation It is matching of signal with a delayed version of itself.

Autocorrelation of real valued Energy Signal

Autocorrelation of a complex Energy Signal:

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Autocorrelation (contd..)

Autocorrelation Properties of Energy Signal

Autocorrelation is symmetric around zero.

Its maximum value occurs at the origin.

Autocorrelation and spectral density form a Fourier transform pair.

Its value at the origin is equal to energy.

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Autocorrelation (contd..)

Real valued Power Signal:

Complex Power Signal :

For a periodic signal:

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Autocorrelation (contd..)

Autocorrelation Properties of Power Signal

Autocorrelation is symmetric around zero.Its maximum value occurs at the origin.Autocorrelation and spectral density form a Fourier transform pair. Its value at the origin is equal to the average power.

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Communication Systems Basband Communication

Baseband signals are used to transmit information. Each message symbol is represented by one of a set of

pulse waveforms g1(t), g2(t)……gM(t) The spectrum of baseband signal lies around the origin in

frequency domain Passband Communication

Passband signals are used to transmit information. Each baseband pulse waveform is represented by one set of

bandpass waveforms s1(t), s2(t)…sM(t) The spectrum is located away from the origin

Data rate It is speed of communication. In case of Binary signaling, it is measured as bits/sec and in

case of M-ary Signaling it is measured as symbols/sec.

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Review (contd..)

Baseband signal

Its spectra ranges from (near ) DC to some finite value

Passband Signal

Its spectrum is shifted away from DC Value

2006-01-24 Lecture 1 44

END