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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
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Objective of Subject
?
?
?
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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?
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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
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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
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CA Evaluation
Assignments
1. Test (Assignment based)
Marks =30
2. Exercise+ Test
Marks 30
3. Test
Marks =30
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Prerequisite Knowledge
Mathematics
Desired
Programing
MATLAB
Python
C/C++
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Logistic
Course Page
Material
Online Group/Forum
Updates
QTT
FUN!!! With MATLAB
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Unit-1: Basics of Signal & Systems
#Refer to Chapter 1 of Oppenheim
Signal???
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What is Signal
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Signal
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1-Dimensional signal- Audio
Speech and Waveforms
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Example
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2-Dimensional signal -Image
Image
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3-Dimensional signal-Video
Video
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Other Examples
Money in your Pocket
Stock Market
Air flow in room
Vision of any object
Many more…
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Systems
What is systems?
Examples
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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.
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Examples of mechanical and
electrical systems
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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
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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)
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Elementary Signals
#Refer to Chapter 1 of Oppenheim
Unit Step Signal
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Unit Impulse Function
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Exponential
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Exponential
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Complex-Exponential
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Exponential
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Practical Case of Step and Impuls
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Gate function
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Signal and transformation
Continues
Discrete
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Signals
Signals
Signal?
Classification of Signals :Properties
Continues & Discrete
Analog & Digital,
Deterministic & Random & chaotic signal
Periodic & Aperiodic
Energy & Power
Even & Odd
Real & Complex
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#Refer to Chapter 1 of OppenheimNikes
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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)”
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Continues and Discrete signal
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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…
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Analog/Digital/Continues/Discrete
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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
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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
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Periodicity
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Periodic Signal
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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 = ________________ _______________
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Energy and Power
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Energy and Power
Energy
Power
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Ref: http://ocw.nctu.edu.tw/
Deductions!!!!-check on http://nikeshbajaj.in/signals-and-systems/
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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 =
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Examples –Solve following
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Ref: http://ocw.nctu.edu.tw/Nikes
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Examples
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Even and Odd
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Even and Odd
Any signal can be broken into two parts, even and
odd
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Real and Complex
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Basic Operation on signal
Shifting : Advancing and Delaying
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Shifting
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Ref: LathiNikes
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Signals & Systems
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