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Networks and Systems

Networks and Systems. Instructors: Prof. V.G.K. Murti, Dr. Andrew Thangaraj, and Prof. C.S. Ramalingam, IIT Madras. Networks, signals and systems form the basic foundations of electrical engineering. Any electrical engineering product handles signals using electrical networks and circuits, which are called systems. Having a good understanding of signals and their time/frequency domain characterization is an absolute must for any electrical engineer. This course is a basic introduction to discrete and continuous-time signals, Fourier series, Fourier transforms and Laplace transforms. (from nptel.ac.in)

Lecture 37 - Energy Considerations (cont.)

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Prerequisites

Prerequisite 01 - Functions in Circuits - Constant and Sinusoidal Functions

Prerequisite 02 - Functions in Circuits - Exponential Functions

Prerequisite 03 - Complex Numbers and Other Topics

Introductory Concepts

Lecture 01 - Systems, Signals, Networks

Lecture 02 - Representation and Classification of Systems

Lecture 03 - Linear Systems

Lecture 04 - Time-Invariance and Causality

Lecture 05 - Signals, Elementary Continuous Signals

Lecture 06 - Complex Frequencies of Signals

Lecture 07 - Discontinuous Signals - Step, Ramp

Lecture 08 - Unit Impulse or Delta Function

Lecture 09 - Basic Discrete-Time Signals

Assignment 01 - Networks and Systems: Solutions to Assignment 1

Lecture 10 - Examples of Signals

Lecture 11 - Introduction to Systems, Complementary Functions, Initial Conditions

Lecture 12 - Special Initial Conditions

Lecture 13 - Characterization of a Linear System

Lecture 14 - Impulse Response

Lecture 15 - Evaluating the Convolution Integral

Lecture 16 - Worked-out Problems

Assignment 02 - Networks and Systems: Hints for Assignment 2

Fourier Series

Lecture 17 - Introduction and Motivation

Lecture 18 - Evaluating Fourier Series Coefficients

Lecture 19 - Symmetry Conditions

Lecture 20 - Symmetry Condition Examples

Lecture 21 - Application to Network Analysis

Assignment 03 - Networks and Systems: Hints for Assignment 3

Lecture 22 - Exponential Fourier Series

Lecture 23 - Frequency Spectrum

Lecture 24 - Frequency Spectrum: Examples

Lecture 25 - Signal Power and Related Ideas

Lecture 26 - Convergence of Fourier Series

Lecture 27 - Additional Properties of Fourier Series

Lecture 28 - Exercises on Fourier Series

Lecture 29 - Demonstration Experiments on Fourier Series

Fourier Transform

Lecture 30 - From Fourier Series to Fourier Transform

Lecture 31 - Continuous Time Fourier Transform

Lecture 32 - Fourier Transform Examples

Lecture 33 - Examples and Some Properties of Fourier Transform

Lecture 34 - Properties of Fourier Transform (cont.)

Lecture 35 - Properties of Fourier Transform (cont.)

Lecture 36 - Energy Considerations

Lecture 37 - Energy Considerations (cont.)

Lecture 38 - Helpful Relationships for Inverse Fourier Transform

Lecture 39 - Fourier Transform of Signals that are Not Absolutely Integrable

Lecture 40 - Fourier Transform of Periodic Signals, Unit Step and Signum Function

Lecture 41 - Fourier Transform of Truncated Sinusoid, Convolution Properties of Fourier Transform

Lecture 42 - Integration in Time Domain

Lecture 43 - Application of Continuous Time Fourier Transform to System Analysis

Lecture 44 - Comments about Transient Analysis

Lecture 45 - Sampling Theorem and Exercises on Fourier Transforms

Laplace Transform

Lecture 46 - Introduction to Laplace Transform

Lecture 47 - Laplace Transforms of Important Functions

Lecture 48 - Poles/Zeros and Laplace Transform Notation

Lecture 49 - Properties: Linearity, Differentiation in the Time Domain

Lecture 50 - Application and Properties of Laplace Transform

Lecture 51 - Properties of Laplace Transform: Shift in Frequency Domain

Lecture 52 - Properties of Laplace Transform: Shift in Time Domain, Scaling

Lecture 53 - Properties: Division by 't' Initial Value Theorem, Final Value Theorem

Lecture 54 - Properties: Convolution in Time Domain

Lecture 55 - Complex Convolution and Periodic Functions

Lecture 56 - Examples of Laplace Transform

Lecture 57 - Examples of Laplace Transform (cont.)

Lecture 58 - Inverse Laplace Transform

Lecture 59a - Partial Fraction Expansion: Multiple Poles (General Case)

Lecture 59b - Inverse Laplace Transform and Contour Integration

Lecture 59c - Relationship between Fourier and Laplace Transforms

Lecture 59d - Exercises on Laplace Transforms

Applications of Laplace Transforms

Lecture 60 - Applications of Laplace Transform to Network Transients

Lecture 61 - Laplace Transform for Resistor and System Analysis

Lecture 62 - Laplace Transform Method for Mutual Inductance

Lecture 63a - Mutual Inductance Example (cont.)

Lecture 63b - Examples and Advantages of Laplace Transform

Lecture 64 - General LTI Systems and The Many Facets of the System Function H(s)

Lecture 65 - The Many Facets of the System Function H(s) (cont.)

Lecture 66 - Frequency Response and Stability

Lecture 67a - System Analysis Example

Lecture 67b - Exercies