lec-1-introduction-and-signals.pdf - WordPress.com

11/5/2014

1

Signal & SystemsIntroduction to course and Signals

Nikesh [email protected]

Digital Signal Processing

School of Electronics and Communication

Lovely Professional University

Signal & SystemsECE220

Overview

Objective of Subject

Syllabus: overview

Reference books, Papers, Journals

Introduction to subject

Prerequisite Knowledge

Review of Basics

Summary

2 By: Nikesh Bajaj

Objective of Subject

?

?

?

By: Nikesh Bajaj3

Why do you need

Signals & Systems??

What this subject bring to you?

What you will be able to do?

How this will make difference?

How important is it?

By: Nikesh Bajaj4

Syllabus

UNITs

Basics of Signal and Systems

LTI Systems

Frequency Domain Representation

Fourier Series and Transform

--------------MTE--------------------------

DTFT and DFT

Laplace Transform

Z- Transform

System realization & Applications

5 By: Nikesh Bajaj

References

Text

Oppenheim, ALAN V, Signals and Systems. Second Edition, PHI Publication,

ISBN: 978-81-203-1246-3

Other Books

SIGNAL AND SYTEMS, SIMON HAYKIN, JOHN WILEY & SONS

Schaums Outline Signal and System by HWEI P.HSU

Signal processing and linear systems, B.P. Lathi , oxford university press

6 By: Nikesh Bajaj

Nikes

h Baja

j

Signals & Systems

11/5/2014

2

CA Evaluation

Assignments

1. Test (Assignment based)

Marks =30

2. Exercise+ Test

Marks 30

3. Test

Marks =30

7 By: Nikesh Bajaj

Prerequisite Knowledge

Mathematics

Desired

Programing

MATLAB

Python

C/C++

8 By: Nikesh Bajaj

Logistic

Course Page

Material

Online Group/Forum

Updates

QTT

FUN!!! With MATLAB

By: Nikesh Bajaj9

Unit-1: Basics of Signal & Systems

#Refer to Chapter 1 of Oppenheim

Signal???

By: Nikesh Bajaj11

What is Signal

By: Nikesh Bajaj12

Nikes

h Baja

j

Signals & Systems

11/5/2014

3

Signal

By: Nikesh Bajaj13

1-Dimensional signal- Audio

Speech and Waveforms

By: Nikesh Bajaj14

Example

By: Nikesh Bajaj15

2-Dimensional signal -Image

Image

By: Nikesh Bajaj16

By: Nikesh Bajaj17

3-Dimensional signal-Video

Video

By: Nikesh Bajaj18

Nikes

h Baja

j

Signals & Systems

11/5/2014

4

Other Examples

Money in your Pocket

Stock Market

Air flow in room

Vision of any object

Many more…

By: Nikesh Bajaj19

Systems

What is systems?

Examples

By: Nikesh Bajaj20

Introduction

System

Examples of signals include :

1 . A voltage signal: voltage across two points varying as a function of

time.

2 . A force pattern: force varying as a function of 2-dimensional space.

3 . A photograph: color and intensity as a function of 2-dimensional space.

4 . A video signal: color and intensity as a function of 2-dimensional space

and time.By: Nikesh Bajaj21

Systems: Examples

Examples of systems include :

1. An oscilloscope: takes in a voltage signal, outputs a 2-dimensional image

characteristic of the voltage signal.

2. A computer monitor: inputs voltage pulses from the CPU and outputs a

time varying display.

3 An accelerating mass : force as a function of time may be looked at as the

input signal, and velocity as a function of time as the output signal.

4 A capacitance: terminal voltage signal may be looked at as the input,

current signal as the output.

By: Nikesh Bajaj22

Examples of mechanical and

electrical systems

By: Nikesh Bajaj23

You are surely familiar with many of these signals and systems and have probably analyzed them as well, but in

isolation . For instance, you must have studied accelerating masses in a mechanics course (see Fig (a)), and

capacitances in an electrostatic course (see Fig (b)), separately

Signals

“Function that depends on some independent

variable”

F(t), F(x,y) etc.

#Refer to Chapter 1 of OppenheimNikes

h Baja

j

Signals & Systems

11/5/2014

5

Classifications

Continues Discrete

Continues: values at every points, independent variable is

continues R e.g. x(t)

Discrete : values at only specific points, independent variable is

discrete Z e.g. x(n)

By: Nikesh Bajaj25

Elementary Signals

#Refer to Chapter 1 of Oppenheim

Unit Step Signal

By: Nikesh Bajaj27

Unit Impulse Function

By: Nikesh Bajaj28

Exponential

By: Nikesh Bajaj29

Exponential

By: Nikesh Bajaj30

Nikes

h Baja

j

Signals & Systems

11/5/2014

6

Complex-Exponential

By: Nikesh Bajaj31 By: Nikesh Bajaj32


Exponential

By: Nikesh Bajaj35

Practical Case of Step and Impuls

By: Nikesh Bajaj36

Nikes

h Baja

j

Signals & Systems

11/5/2014

7

Gate function

By: Nikesh Bajaj37

Signal and transformation

Continues

Discrete

By: Nikesh Bajaj38


By: Nikesh Bajaj41

Signals

Signals

Signal?

Classification of Signals :Properties

Continues & Discrete

Analog & Digital,

Deterministic & Random & chaotic signal

Periodic & Aperiodic

Energy & Power

Even & Odd

Real & Complex

42 By: Nikesh Bajaj

#Refer to Chapter 1 of OppenheimNikes

h Baja

j

Signals & Systems

11/5/2014

8

Continues and Discrete signals

Continues Signal If independed variable of function is continues variable (R, it can take

any value), function (or signals) is called as continues signal

f(t) =sin(2t) (t R) can take any value

“Signal can have values for any given instance of time (or variable)”

Discrete Signal If independed variable of function is discrete variable (it can take only

certain value), function (or signals) is called as dicrete signal

f(n) =sin(2n) (n Z) can take only ..-2-10 +1 +2

“Signal can have values for only discrete instance of time (or

variable)”

By: Nikesh Bajaj43

Continues and Discrete signal

By: Nikesh Bajaj44

Analog and Digital

Analog If function (Amplitude) have infinite set of values, it is called

Analog signal

f(t) =sin(2t) f(t) R

Digital

If function (Amplitude) have finite set of values, it is

called Analog signal

If f(n) can have only two values (0, 1) it is binary

If f(n) can have only three values (0, 1,2) it is ternary

And so on…

By: Nikesh Bajaj45

Analog/Digital/Continues/Discrete

By: Nikesh Bajaj46

Don’t be

Don’t be confused with

Analog and Continues and

Digital with Discrete

Analog signal can be Continues as well as

discrete

Similarly a digital signal can be Continues as

well as discrete

By: Nikesh Bajaj47

Deterministic and Random

Deterministic Signal have mathematical model/equation

Values of signal can be computed for any instances

f(t) =sin(2t) or f(n) =sin(2n)

Random Signal do not have mathematical model/equation

Values of signal can NOT be computed for any instances

Example: speech, noise etc

Chaotic signals

Roughly: Signal which have mathematical model and equations

but behave like random, called as chaotic. By: Nikesh Bajaj48

Nikes

h Baja

j

Signals & Systems

11/5/2014

9

Periodicity

By: Nikesh Bajaj49

Periodic Signal

By: Nikesh Bajaj50



Nikes

h Baja

j

Signals & Systems

11/5/2014

10

Deductions!!!-check on http://nikeshbajaj.in/signals-and-systems/

Deduce following with possible answers as “Always/Not Always

+ Periodic/Aperiodic ” Answers will be different for Continues Time and Discrete

Time Signals So answer separately for Continues and Discrete

Cases Continues Discrete

Periodic + Periodic = ________________ _______________ (+ and -)

Periodic + Aperiodic = ________________ _______________

Aperiodic + Aperiodic = ________________ _______________

Periodic x Periodic = ________________ _______________

Periodic x Aperiodic = ________________ _______________

Aperiodic x Aperiodic = ________________ _______________

By: Nikesh Bajaj55

Energy and Power

By: Nikesh Bajaj56

Energy and Power

Energy

Power

By: Nikesh Bajaj57

Ref: http://ocw.nctu.edu.tw/

Deductions!!!!-check on http://nikeshbajaj.in/signals-and-systems/

By: Nikesh Bajaj58

1. All Time limited* signals are ALWAYS Energy Signals EXCEPT signals

does not blow up* in between

2. All Time unlimited** signals ALWAYS have Infinite

Energy EXCEPT signal tends to zero when it approaches to infinity

3. All Periodic Signals have infinite Energy

4. All Periodic Signals are ALWAYS Power signals EXCEPT signal does not

blow up in any period

*Time Limited means signal exist from t1 to t2 only (for finite time duration

only) **Time Unbounded mean At least one limit of signal touches to infinity.

Signal exist either from – infinity to + infinity, t1 to +infinity or -infinity to t1

Energy and Power Signal

Energy Signal

Signal with finite energy E< is called energy signal

It has 0 average power P=0

Power Signal

Signal with infinite Energy E= and finite average

Power P< is called Power Signal

Neither Energy nor Power signal

Signal with infinite energy and Infinite power falls in

this category

E = & P =

By: Nikesh Bajaj59

Examples –Solve following

By: Nikesh Bajaj60

Ref: http://ocw.nctu.edu.tw/Nikes

h Baja

j

Signals & Systems

11/5/2014

11

Examples

By: Nikesh Bajaj61

Even and Odd

By: Nikesh Bajaj62

Even and Odd

Any signal can be broken into two parts, even and

odd

By: Nikesh Bajaj63

Real and Complex

By: Nikesh Bajaj64

Basic Operation on signal

Shifting : Advancing and Delaying

By: Nikesh Bajaj65

Shifting

By: Nikesh Bajaj66

Ref: LathiNikes

h Baja

j

Signals & Systems

11/5/2014

12

Scaling: Compression and Expansion

Or Speedup & Slow-downed

By: Nikesh Bajaj67

Scaling

By: Nikesh Bajaj68

Ref: Lathi

Time reversal

By: Nikesh Bajaj69

Time Reversal

By: Nikesh Bajaj70

Ref: Lathi

Useful Formulas

By: Nikesh Bajaj71

Nikes

h Baja

j

Signals & Systems

lec-1-introduction-and-signals.pdf - WordPress.com

Documents

Transcript of lec-1-introduction-and-signals.pdf - WordPress.com