Undergraduate Course On Signals And Systems-I

Fundamentals of signal processing in Continuous time domain and in Discrete time domain

What you'll learn

Basic definitions of Continuous and discrete signals and opertions on time

Periodic and aperiodic signals

Energy and power signals

Even and odd signals

Singularity functions like unit impulse, unit step and unit impulse signals

System defintion and properties

Basic convolution in continuous and discrete time domains

Requirements

Basic Mathematics

Description

This is an undergraduate course on signals and systems. This course is first one in a series of two courses on basics of signals and systemsFor any electrical, electronics, Instrumentation or bio-medical engineering student understanding basics of signals in continuous time(CT) domain and in discrete time(DT) domain is a must. This course gives an in-depth coverage of all the fundamentals required for signal processing in both the domains. This can also be taken as a refresher course to understand 'Digital signal processing'.The organisation and coverage of topics is as follows:Introduction to signals: This module begins with basic definition of signal and system. The primary classification of signals and independent variables in signal representation are well explained. Then we will move on to the operations performed on independent variable like time and their order of precedence. Classification of signals: Periodic and aperiodic signal classification is explained with sinusoidal signals and real exponential signals in detail. Another classification energy and power signals is given with all necessary examples. Finally, even and odd signals classification and its extension conjugate symmetric and conjugate anti symmetric signal classification is explained. Standard signals: An in-depth coverage of  singularity functions like unit-impulse, unit-step and unit-ramp signals are given in this chapter. All these signals are defined graphically and mathematically in both CT and DT domains. Properties of signals and relation between singularity functions is also explained. And other signals like signum function, sinc function etc., are also covered.System properties: All the system properties that is Linearity, time invariance, causality, stability, memory and invertibility are well explained with standard examples.About Author:Mr. Udaya Bhaskar is an undergraduate university level faculty and GATE teaching faculty with more than 16 years of teaching experience. His areas of interest are signal processing, semiconductors, digital design and other fundamental subjects of electronics.  He trained thousands of students for GATE and ESE examinations.

Overview

Section 1: Introduction

Lecture 1 Definition of signal and system

Lecture 2 Independent Variables- Time and frequency

Lecture 3 Note on independent variables

Lecture 4 Primary classification of signals

Lecture 5 Construction of a discrete domain signal

Lecture 6 Finite duration sequence and definition of sampling and interpolation

Lecture 7 Time shifting operation-01

Lecture 8 Time shifting operation-02

Lecture 9 Time scaling operation in CT domain

Lecture 10 Time compression in DT domain

Lecture 11 Time expansion in DT domain-01

Lecture 12 Time expansion in DT domain-02

Lecture 13 Time inversion

Lecture 14 Amplitude inversion

Lecture 15 Order of precedence in CT domain

Lecture 16 Order of precedence in DT domain

Lecture 17 Solved example-01

Lecture 18 Solved example-02

Lecture 19 Solved example-03

Lecture 20 Solved example-04

Section 2: Classification of signals

Lecture 21 Periodic signal construction

Lecture 22 Periodic signal- fundamental period and fundamental frequency

Lecture 23 Periodic signal in DT domain

Lecture 24 Summation of periodic signals

Lecture 25 Solved example-01

Lecture 26 Example for periodic signal-Sinusoidal signals

Lecture 27 Sinusoidal signals in DT domain

Lecture 28 L28

Lecture 29 Difference between CT and DT domain sinusoidal signals-01

Lecture 30 Difference between CT and DT domain sinusoidal signals-02

Lecture 31 Solved example-02

Lecture 32 Solved example-03

Lecture 33 Solved example-04

Lecture 34 Solved example-05

Lecture 35 Solved example-06

Lecture 36 Solved example-07

Lecture 37 Example for aperiodic signals- real exponential signal

Lecture 38 Real exponential signals in DT domain

Lecture 39 Engery and power signal- Basic definitions

Lecture 40 Energy and power signal- Mathematical expressions

Lecture 41 Energy and power expressions-Summary

Lecture 42 Root Mean Square(RMS) value

Lecture 43 Operations performed on energy signal

Lecture 44 Operations performed on power signal

Lecture 45 Average power calculation of sinusoidal signals-01

Lecture 46 Average power calculation of sinusoidal signals-02

Lecture 47 Solved example-08

Lecture 48 Solved example-09

Lecture 49 Solved example-10

Lecture 50 Solved example-11

Lecture 51 Even and Odd signals-Definition

Lecture 52 Real signal as a combination of even and odd signals

Lecture 53 Area of even and odd signals

Lecture 54 Conjuage symmetric and Conjuage anti symmetric signals

Lecture 55 CS and CAS signals(contd….)

Lecture 56 Solved example-12

Lecture 57 Solved example-13

Lecture 58 Solved example-14

Lecture 59 Solved example-15

Section 3: Standard signals

Lecture 60 Unit impulse signal in CT and DT domains

Lecture 61 Area of unit impulse

Lecture 62 Sampling property

Lecture 63 Sampling property in DT domain

Lecture 64 Sifting property

Lecture 65 Scaling property

Lecture 66 Differentiation property

Lecture 67 Impulse train

Lecture 68 Discrete time signal as combination of impulses

Lecture 69 Continuous time signal as combination of impulses

Lecture 70 Solved example-01

Lecture 71 Solved example-02

Lecture 72 Solved example-03

Lecture 73 Solved example-04

Lecture 74 Unit step signal definition

Lecture 75 Practice step signal

Lecture 76 Unit step scaling

Lecture 77 Energy and power of step signal

Lecture 78 Even and Odd components of unit step signal

Lecture 79 Combination of step signals

Lecture 80 Causal signal definition wrt to step signal

Lecture 81 Causal signals in DT domain

Lecture 82 Causality condition-examples

Lecture 83 Significance of step signal

Lecture 84 Energy calculation for real exponential signals

Lecture 85 Energy of real exponential signals-summary

Lecture 86 Energy of real exponential signals in DT domain

Lecture 87 Relation between unit step and unit impulse-01

Lecture 88 Relation between unit step and unit impulse-02

Lecture 89 Relation between step and impulse-Summary

Lecture 90 Signum function

Lecture 91 Solved example-05

Lecture 92 Solved example-06

Lecture 93 Solved example-07

Lecture 94 Solved example-08

Lecture 95 Solved example-09

Lecture 96 Solved example-10

Lecture 97 Unit ramp signal definition

Lecture 98 Ramp signal scaling

Lecture 99 Combination of ramp signals

Lecture 100 Triangular pulse

Lecture 101 Relation between ramp-step-impulse

Lecture 102 Solved example-11

Lecture 103 Solved example-12

Lecture 104 Sinc function and Sampling function

Lecture 105 Sinc function in discrete time domain

Section 4: System properties

Lecture 106 System properties

Lecture 107 Linearity

Lecture 108 Linearity graphical representation

Lecture 109 Step by step procedure for finding linearity of a system

Lecture 110 Linearity- standard example set-01

Lecture 111 Linearity- standard example set-02

Lecture 112 Linearity-standard example set-03

Lecture 113 Linearity- standard example set-04

Lecture 114 Linearity-Special case

Lecture 115 Time invariance-definition

Lecture 116 Procedure to determine time invariance

Lecture 117 Time invariance-Standard example set-01

Lecture 118 Time invariance-Standard example set-02

Lecture 119 Time invariance-Standard example set-03

Undergraduate engineering students with Electrical engineering, Electronics engineering, Biomedical engineering, Instrumentation engineering as specialisation,Diploma/Polytechnic students with Electronics engineering, Communication engineering, Instrumentation as specialisation,GATE and PSU preparing students,Any Electronics or communication engineer who wants strengthen signal processing fundamentals