The Fourier Transform and its Applications

Stanford University , Prof.Brad Osgood

Fourier series

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Course Description

Contents:
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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