Stanford / Engineering / Electrical
Lecture : Summary Of Previous Lecture (Analyzing General Periodic Phenomena As A Sum Of Simple Periodic Phenomena)
By Brad Osgood | The Fourier Transform and its Applications
Lecture 3 of 30
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 More Lectures - Select Lecture...1 : Previous Knowledge Recommended (Matlab)2 : Periodicity; How Sine And Cosine Can Be Used To Model More Complex Functions3 : Summary Of Previous Lecture (Analyzing General Periodic Phenomena As A Sum Of Simple Periodic Phenomena)4 : Wrapping Up Fourier Series; Making Sense Of Infinite Sums And Convergence5 : Continued Discussion Of Fourier Series And The Heat Equation6 : Correction To Heat Equation Discussion7 : Review Of Fourier Transform (And Inverse) Definitions8 : Effect On Fourier Transform Of Shifting A Signal9 : Continuing Convolution: Review Of The Formula10 : Central Limit Theorem And Convolution; Main Idea11 : Correction To The End Of The CLT Proof12 : Cop Story13 : Setting Up The Fourier Transform Of A Distribution14 : Derivative Of A Distribution15 : Application Of The Fourier Transform: Diffraction: Setup16 : More On Results From Last Lecture (Diffraction Patterns And The Fourier Transforms)17 : Review Of Main Properties Of The Shah Function18 : Review Of Sampling And Interpolation Results19 : Aliasing Demonstration With Music20 : Review: Definition Of The DFT21 : Review Of Basic DFT Definitions22 : FFT Algorithm: Setup: DFT Matrix Notation23 : Linear Systems: Basic Definitions24 : Review Of Last Lecture: Discrete V. Continuous Linear Systems25 : Review Of Last Lecture: LTI Systems And Convolution26 : Approaching The Higher Dimensional Fourier Transform27 : Higher Dimensional Fourier Transforms- Review28 : Shift Theorem In Higher Dimensions29 : Shahs30 : Tips For Filling Out Evals

Course Description
The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. Together with a great variety, the subject also has a great coherence, and the hope is students come to appreciate both.

Topics include: The Fourier transform as a tool for solving physical problems. Fourier series, the Fourier transform of continuous and discrete signals and its properties. The Dirac delta, distributions, and generalized transforms. Convolutions and correlations and applications; probability distributions, sampling theory, filters, and analysis of linear systems. The discrete Fourier transform and the FFT algorithm. Multidimensional Fourier transform and use in imaging. Further applications to optics, crystallography. Emphasis is on relating the theoretical principles to solving practical engineering and science problems.
Courses Index
2 : Introduction to Digital Integrated Circuits   (Jan RABAEY / Berkeley)
4 : Introduction to Microelectronic Circuits   (Bernhard BOSER / Berkeley)
5 : Introduction to Linear Dynamical Systems   (Stephen Boyd / Stanford)
6 : Convex Optimization I   (Stephen Boyd / Stanford)
7 : Convex Optimization II   (Stephen Boyd / Stanford)
8 : Circuits and Electronics   (Anant Agarwal / MIT)
9 : Computer System Engineering   (Samuel Madden / MIT)
10 : Introduction to Algorithms   (Erik Demaine / MIT)
11 : Principles of Digital Communications I   (Lizhong Zheng / MIT)
12 : Principles of Digital Communication II   (David Forney / MIT)
13 : Understanding Lasers and Fiberoptics   (Shaoul Ezekiel / MIT)
14 : Electromagnetics and Applications   (Multiple Instructors / MIT)
15 : Information and Entropy   (Paul Penfield / MIT)
16 : Fundamentals of Laser   (Sabieh Anwar / LUMS)
17 : Synchrotron Radiation for Materials Science   (David Attwood / Berkeley)
18 : Linear Integrated Circuits   (Clark Nguyen / Berkeley)
19 : Digital Circuit Design   (Ken Boyd / University of New South Wales)
20 : Speech and Audio Processing   (Multiple Multiple / University of New South Wales)