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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)

Systems, Signals, Networks


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

References
Networks and Systems
Instructors: Prof. V.G.K. Murti, Dr. Andrew Thangaraj, and Prof. C.S. Ramalingam, IIT Madras. This course is a basic introduction to discrete and continuous-time signals, Fourier series, Fourier transforms and Laplace transforms.