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The Fourier Transform and its Applications

Lecture 1: Fourier series

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Course Description :

Fourier series - Periodicity; How Sine And Cosine Can Be Used To Model More Complex Functions - Analyzing General Periodic Phenomena As A Sum Of Simple Periodic Phenomena - Wrapping Up Fourier Series; Making Sense Of Infinite Sums And Convergence - Continued Discussion Of Fourier Series And The Heat Equation - Correction To Heat Equation Discussion - Review Of Fourier Transform (And Inverse) Definitions - Effect On Fourier Transform Of Shifting A Signal-Continuing Convolution: Review Of The Formula - Central Limit Theorem And Convolution; Main Idea - Correction To The End Of The CLT Proof-Cop Story - Setting Up The Fourier Transform Of A Distribution - Derivative Of A Distribution-Application Of The Fourier Transform: Diffraction: Setup

More On Results From Last Lecture - Review Of Main Properties Of The Shah Function - Review Of Sampling And Interpolation Results - Aliasing Demonstration With Music - Review: Definition Of The DFT - Review Of Basic DFT Definitions - FFT Algorithm: Setup: DFT Matrix Notation - Linear Systems: Basic Definitions-Discrete Vs Continuous Linear Systems - LTI Systems And Convolution - Approaching The Higher Dimensional Fourier Transform-Higher Dimensional Fourier Transforms - Review - Shift Theorem In Higher Dimensions - Shahs - Tomography And Inverting The Radon Transform

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