# InfoCoBuild

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

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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