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Fourier Transform and Applications

Lecture series on the Fourier Transform, Fourier series and applications, by Prof Brad Osgood at Stanford Univ EE 261

Introduction and Table of Contents

This video series is entitled, "Fourier Transform and Applications," which provides lecture series on the Fourier Transform, Fourier series and applications, by Prof Brad Osgood at Stanford Univ EE 261. The series presents 30 individual lectures and span the subject of Fourier Transforms. These videos have a total playtime duration of 1 dys 01 hrs 38 min 03 sec.

Lecture series by Professor Brad Osgood, of Stanford University, Dept of Engineering, for the Electrical Engineering course, "The Fourier Transforms and its Applications" (EE 261). The Fourier transform is a tool for solving physical problems. In this course the emphasis is on relating the theoretical principles to solving practical engineering and science problems.

These lessons are useful for math, physics, chemistry, engineering, geology, and even biology students, due to the diverse applications of the Fourier transform. The Fourier Transforms and its Applications course lessons begin on Fourier series, covers the Fourier transform, and many of it's applications, as a tool for solving science, physical and engineering problems. Prerequisites: Math through calculus and ordinary differential equations (ODE's), basic linear algebra, Comfort with sums and discrete signals (would be ideal), Fourier series at the level of 102A.

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Fourier Transforms: Fourier Transform and Applications

LLecture titles for Fourier Transform and ApplicationsTimeNote
1Fourier Transforms, simple functions, sin(t), cos(t), model periodic phenomenon, how to do it, analyzing general periodic phenomenon52:07
2Fourier Transforms, simple functions, sin(t), cos(t), model periodic phenomenon, how to do it, analyzing general periodic phenomenon52:57first steps in analyzing general periodic phenomenon
3Fourier Transforms, analysis of periodic phenomena and how it's represented, applications, how to do it, mathematics, waves, analysis50:46
4Fourier Transforms, theoretical aspects of Fourier Series, heat flow, applications, how to do it, mathematics, waves, analysis52:07application to heat flow
5Fourier Transforms, Fourier series, transformation Fouier series compared to Fourier transformations, periodic phenomena, non-periodic phenomena, limiting process, applications, how to do it52:01periodic phenomena to non-periodic phenomena by means of a limiting process
6Formal treatment of Fourier Transforms, Fourier transformations, applications, how to do it, mathematics, waves, analysis47:52
7Fourier Transforms, inverse of the Fourier transform, applications, how to do it, mathematics, waves, analysis47:49specific properties and transforms
8Fourier Transforms, general properties, two paths, develop specific transforms, different combinations, functions, applications, how to do it, mathematics, waves, analysis50:37Fourier transforms with different combinations and functions
9convolution, signal combinations, Fourier Transforms, convolution, signal combinations, applications, how to do it, mathematics, waves, analysis54:23
10Fourier Transforms, operation of convolution, central limit theorem, applications, how to do it, mathematics, waves, analysis54:58
11Fourier Transforms, convergence of intervals, applications, how to do it, mathematics, waves, analysis50:56
12Rapidly decreasing functions, best Fourier Functions, Fourier Transforms, applications, how to do it, mathematics, waves, analysis52:56
13Fourier Transforms, general distributions, applications, how to do it, mathematics, waves, analysis49:25
14Fourier Transforms, distributions, applications, how to do it, mathematics, waves, analysis54:00
15Fourier Transforms, deltas, properties of deltas, physical interpretation of deltas, applications, how to do it, mathematics, waves, analysis52:09
16Fourier Transforms, sampling, interpolation, diffraction, applications, how to do it, mathematics, waves, analysis49:43diffraction
17Fourier Transforms, sampling, interpolation, associated properties, applications, how to do it, mathematics, waves, analysis41:13
18Fourier Transforms, sampling, interpolation, associated phenomena, applications, how to do it, mathematics, waves, analysis51:09
19Fourier Transforms, aliasing, under sampling, music, applications, how to do it, mathematics, waves, analysis52:06
20Discrete Fourier Transforms, applications, how to do it, mathematics, waves, analysis52:53
21Discrete Fourier Transforms, applications, how to do it, mathematics, waves, analysis52:59
22Fast Fourier Transforms algorithm, applications, how to do it, mathematics, waves, analysis51:16
23Fourier Transforms, linear systems, linear time, variance systems, applications, how to do it, mathematics, waves, analysis51:04
24Fourier Transforms, linear systems, applications, how to do it, mathematics, waves, analysis57:05
25relationship between LTI and the Fourier transforms, Fourier Transforms, applications, how to do it, mathematics, waves, analysis53:17LTI systems
26Final topic, space, higher dimension Fourier Transforms, applications, how to do it, mathematics, space and the higher dimension Fourier Transform53:56
27higher dimension Fourier Transforms, applications, how to do it, mathematics, higher dimension Fourier Transform49:57
28higher dimensional Fourier Transforms, applications, how to do it, mathematics, higher dimensional Fourier Transforms49:07
29general stretch theorem, medical imaging, Fourier Transforms, applications, how to do it, mathematics, general stretch theorem, medical imaging50:06
30tomography, inverting the radon transform in medical imaging, Fourier Transforms, applications, how to do it, mathematics47:09
 Total Time of these Lectures = 1:01:38:03  
 

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1:01:38:03 Time (days : hours : minutes : seconds)
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