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CommunicationSystemsLecture 2

Engr. Zaid Ahmad

Department ofTelecommunication EngineeringIqra University, Karachi

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Lecture Objectives

To be familiar with nature and size ofsignals

To understand basic measures of sizeof signal

To learn various criteria forclassification of signals

To learn basic operations on signals

To study some useful fucntions

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Signals

A set of information or data

May be function of time or function ofspace

Function of time, e.g. a telephone ora television signal, daily closingprices of a stock market

Function of space, e.g. surfacecharge density

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Systems

An entity thatprocesses a set ofsignals (inputs) to yield another setof signals (outputs)

Modify signals or extract additionalinformation from them

E.g. by properly processing the radar

signal (the input), we canapproximately estimate the futurelocation (output) of the target

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Systems(2)

Hardware realization of a systemmeans physical components

E. g. electrical, mechanical, hydraulic

Software realization of a systemmeans an algorithm

E. g. image processor

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Size of a Signal

Specified by signal amplitude andsignal duration

Signal Energy and Signal Power

Size of a personhis volume V

=H

dhhrV

0

2 )(

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Signal Energy (Eg)

Area under the squared value g2(t) ofa signal g(t)

Real-valued signal

Complex valued signal

Must be finite or convergent

Amplitude 0 as |t| (Necessarycondition for convergence)

dttgEg )(2

=

dttgEg

=2

)(

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Power (Pg)

Used when Eg=

Time average of the energy Real valued signal: Complex valued signal:

Mean-squared value ofg(t)

Exists if signal is periodic or it hasstatistical regularity Ramp signal g(t)=t is neither energy

nor power signal

dttgT

PT

TT

g )(1

lim

2/

2/

2

=

=

2/

2/

2)(

1lim

T

TT

g dttgT

P

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Signal with Finite Energy orFinite Power

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Signal with Finite Energy orFinite Power

Signal energy and signal power do notindicate actual energy and actualpower

Actual energy dissipated:

Actual Power:

Assume R=1 to take it as Signal Energyand Signal Power

REdt

Rtg g=

)(2

R

Pdt

R

tg

T

gT

TT

=

2/

2/

2 )(1lim

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Applications and Units

Goodness of approximation Comparisons of approximations Judgment of quality of reception by

relative sizes of the desired signal andundesired signal Units depend upon the nature of the

signal (voltage or power)

Energy measured in Square VoltsSecond or Square Ampere Seconds Power measured in Square Volts or

Square Seconds

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Classification of Signals

Continuous-time: Specified for everyvalue of time

Discrete-time: Specified at discrete

values of time Analog: Amplitude may take any value

Digital: Amplitude can take finite

number of values Periodic and Aperiodic Signals

Energy and Power Signals

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Classification of Signals (2)

Periodic Signals: g(t)= g(t)+To forall t, To>0

min (To)=Period

Periodic signal must start at t= -and continue forever

g(t) can be generated by periodicextension of any segment ofg(t) ofduration equal to the period

The above discussion does not hold

for aperiodicsignal

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Classification of Signals (3)

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Classification of Signals (4)

Energy Signal:

Power Signal:

Every real-life signal is an Energysignal

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Classification of Signals (5)

Deterministic Signals: Knowncompletely in mathematical orgraphical form

Random Signals: Known in terms ofprobabilistic measures likemeasures of central tendency or

measure of spread Noise and all message signals are

random

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Signal Operations (Time-Shifting)

To time-shift a signal g(t) by T, replacetwith t-T

g(t) g(t-T)

Delay or Right Shift: T> 0

Advance or Left Shift: T< 0

g(t-2): left-shifted (delayed) g(t) by 2seconds (T=2> 0)

g(t+2): right-shifted (advanced) g(t)by 2 seconds (T=-2 < 0)

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Signal Operations (Time-Shifting) (2)

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Signal Operations (Time-Scaling)

Compression or expansion in time

g(at) compression of g(t) by a

g(t/a) expansion of

g(t) by a

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Signal Operations (Time-Scaling) (2)

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Signal Operations (Time-Reversal)

Time-reversal orTime-inversion

Replace tby t

Frame of reference is rotated by 180o

around vertical axis

g(t) g(-t)

Not same as g(t)

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Signal Operations (Time-Reversal) (2)