# Signals and Systems

Other Course , Prof. S.C. Dutta Roy

### Lecture 1: Introduction to the Course and Basic Concepts

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##### Course Description :

Contents:
Introduction to the Course and Basic Concepts - Signals & their Transportation - Elementary Signals in the Discrete Time Domain - Characterisation of Signals - Basic concepts of Linear Time Systems - Convolution Invertibility, & Stability Causality - Stability Unit, Step Response and Differential Equations - Systems Described by Differential & Difference Equations - Fourier & His Series - More About Fourier Series (With Uncomfortable Questions) - Those Uncomfortable Questions about the Existence of Fourier & Series and Some More

Introduction to Fourier Transform - Fourier Transform of Periodic Function & Fourier Transform Properties - More Properties of Fourier Transformation - Anatomy of a Class Test & a Continued Look at the Properties of F.T - Modulation, Convolutions and Other Interesting Properties of F.T - A Deeper Look at the Modulation Property of F.T - Fourier Analysis of Discrete Time Signals & Systems - The Beginning - More About Fourier Transform of Discrete Time Signals

Further Look into the Properties of DTFT - Convolution, Modulation & Other Properties of DTFT - Farewell to Discrete Time Fourier Transform & Introduction to Sampling - More About Sampling - Introduction to Laplace Transform - Region of Convergence of Laplace Transform & Properties of Laplace Transform - Properties of Laplace Transform (Contd.) - Concluding Discission on Laplace Transform - Introduction to Z Transform - Properties of Z Transform - Further Discussion on Properties of Z Transform

Solution to Class Test - 2, Concluding Discussion on Z Transform - Introduction to Random Signals & Probability - Probability Functions - Solutions to Minor Z Problems & more about PDF & pdf - More About PDF'S & pdf's - Classification of Random Processes & Introduction to Correlation Functions - More About Correction Functions - Cross Correlation Function and their Properties - Introduction to Spectral Density - More About Spectral Density - Response of Linear System to Random Inputs - Frequency Domain Analysis of LTI Systems Excited by Random Inputs.

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