signal representation & analysis introduction

8/12/2019 Signal Representation & Analysis Introduction

1/21


2/21

Content Syllabus

Books to refer

Representation of signals

a) signals and its classification

b) system and its classification


3/21

syllabus


4/21

Representation of signals

Analogy between vectors and signals

Fourier series

Fourier transforms Properties of Fourier transform

Co-relation

Representation aperiodic signal

Convolution property

Hilbert transform

Noise

Signal representation & analysis


5/21


6/21


7/21

Representation ofsignals


8/21

Signal A Signal is defined as information carrying

function.

(or)

A signal is defined as a function of time that

represents a physical variable associated withsystem. the signals are function of one or moreindependent variable and which carry certaininformation about the behavior or nature ofphenomenon.

Ex:- traffic signals, speech signal,ECG.


9/21

Characteristic of signal

More than one variable

eg: 1) speech signal -1D

2) image signal - 2D

3) T.V picture - 3D

4) temperature - 4D

Randomness

Bandwidth


10/21

Types of signals

Continuous signal(analog) : signal which is

defined at any time. both time and

amplitude.

t

f(t)

f(t) = e-2t u(t)


11/21

continuous amplitude , discrete in time

(integer values).

f(nT) = e-2nT u(nT)

t

f(t)

1 2 3 4 5 6 7 8 9

Discrete signal:


12/21

Digital signal:

signal which is discrete both in time and

amplitude is digital signal.

5

4

32

1

1 2 3 4 5 6 7 8 9


13/21

Classification of signals

Even and odd signals

Energy and power signals

Time variant and time invariant signals

Periodic and aperiodic signals


14/21

It is an operator which matches relationbetween input and output.

Lumped and Distributive

Time invariant and Time variant

Linear and non-linear

Causal and non causal Static and dynamic

Stable and unstable

Invertible and non-invertible

Systems

T{ }x(t) Y(t)


15/21

Lumped system

In a lumped system the energy in

a system is considered to be

stored or dissipated in a isolatedelement i.e, R,L,C.it is assumed

that disturbance at an point is

propagated instantaneously atevery point in a system.


16/21

Distributive system

In such system it takes a finite

amount of time for disturbance at

one point to be propagate to theother point.

ex: transmission

lines,anteenas,wave guide.


17/21

Time variant & time invariant

The system whose parameter

change with time is known as

time variant.The response of the system do not

change with time is time

invariant.


18/21

Linear and non-linear

Additive

x1(t) y1(t)

x2(t) y2(t)

x1(t)+x2(t) y1(t)+y2(t)

Homogeneity (scaling)

ax(t) ay(t)

x1(t)+x2(t)y1(t)+y2(t)


19/21

Causal and non causal

A system is causal if the present output

depends on the present input and past

values of the input but not on future

values.ex: y(t)=x2(t)

y(t)=sin[x(t)]

y(t)=x(7-t)
http://localhost/var/www/apps/conversion/tmp/scratch_8/STANDARD%20SIGNALS%20and%20convolution.ppt


20/21

Static and dynamic

A system is static(memoryless) if thepresent output depends on present inputat the same time.

eg: y(t)=x3

(t) Dynamic (memory)

Any differential term in the equation systemis dynamic,due to energy storing

elements.eg: y(t)= dx(t)/dt

All static systems are causal.


21/21

Invertible and non-invertible

A system is invertible if different input leads

to different outputs that is for a given

system two different inputs should not

produce same output.

signal representation & analysis introduction

Documents