The Fourier Transforms and Its Applications
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Brad OsgoodThe Fourier Transforms and Its ApplicationsScienceStanfordENnoThe 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.false1. Fourier Transforms Lecture 1Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood provides an overview of the course, then begins lecturing on Fourier series.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood provides an overview of the course, then begins lecturing on Fourier series.4331557778Tue, 22 Jul 2008 12:03:37 GMTBrad Osgood0:52:06ScienceStanfordno12. Fourier Transforms Lecture 2Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood's lecture addresses the question- How can we use such simple functions, sin(t) and cos(t) to model such periodic phenomenon? He takes the students through the first steps in analyzing general periodic phenomenon.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood's lecture addresses the question- How can we use such simple functions, sin(t) and cos(t) to model such periodic phenomenon? He takes the students through the first steps in analyzing general periodic phenomenon.4331557784Tue, 22 Jul 2008 12:00:01 GMTBrad Osgood0:52:56ScienceStanfordno23. Fourier Transforms Lecture 3Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues lecturing on the analysis of periodic phenomena and how it is represented.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues lecturing on the analysis of periodic phenomena and how it is represented.4331557790Tue, 22 Jul 2008 11:55:06 GMTBrad Osgood0:50:45ScienceStanfordno34. Fourier Transforms Lecture 4Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood wraps up the theoretical aspects of the Fourier Series, an application to heat flow.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood wraps up the theoretical aspects of the Fourier Series, an application to heat flow.4331557796Tue, 22 Jul 2008 11:52:19 GMTBrad Osgood0:52:06ScienceStanfordno45. Fourier Transforms Lecture 5Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood finishes up on Fourier series, then he talks about the transformation Fourier series compared to the Fourier Transform.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood finishes up on Fourier series, then he talks about the transformation Fourier series compared to the Fourier Transform.4331557802Tue, 22 Jul 2008 11:47:18 GMTBrad Osgood0:52:00ScienceStanfordno56. Fourier Transforms Lecture 6Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood picks up where he left off last lecture on Fourier Transformations, then he launches into a more formal treatment of Fourier transforms and explains how to proceed.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood picks up where he left off last lecture on Fourier Transformations, then he launches into a more formal treatment of Fourier transforms and explains how to proceed.4331557808Tue, 22 Jul 2008 11:44:30 GMTBrad Osgood0:47:51ScienceStanfordno67. Fourier Transforms Lecture 7Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood reintroduces the Fourier Transform and its inverse, then he goes into specific properties and transforms.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood reintroduces the Fourier Transform and its inverse, then he goes into specific properties and transforms.4331557814Tue, 22 Jul 2008 11:41:47 GMTBrad Osgood0:47:48ScienceStanfordno78. Fourier Transforms Lecture 8Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues lecturing on the general properties of the Fourier Transforms by two paths. First, to develop specific transforms and second, to understand the Fourier transforms with different combinations and functions.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues lecturing on the general properties of the Fourier Transforms by two paths. First, to develop specific transforms and second, to understand the Fourier transforms with different combinations and functions.4331557820Tue, 22 Jul 2008 11:39:08 GMTBrad Osgood0:50:36ScienceStanfordno89. Fourier Transforms Lecture 9Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on convolution and recaps on Fourier transformations and signal combinations.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on convolution and recaps on Fourier transformations and signal combinations.4331557826Tue, 22 Jul 2008 11:34:38 GMTBrad Osgood0:54:22ScienceStanfordno910. Fourier Transforms Lecture 10Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood introduces the final operation of convolution to the central limit theorem.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood introduces the final operation of convolution to the central limit theorem.4331557832Tue, 22 Jul 2008 11:31:44 GMTBrad Osgood0:54:57ScienceStanfordno1011. Fourier Transforms Lecture 11Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on confronting the convergence of intervals.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on confronting the convergence of intervals.4331557838Tue, 22 Jul 2008 11:28:50 GMTBrad Osgood0:50:55ScienceStanfordno1112. Fourier Transforms Lecture 12Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood reminds the students that the best class of functions for Fourier Functions are rapidly decreasing functions.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood reminds the students that the best class of functions for Fourier Functions are rapidly decreasing functions.4331557844Tue, 22 Jul 2008 11:25:04 GMTBrad Osgood0:52:55ScienceStanfordno1213. Fourier Transforms Lecture 13Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). In this lecture, Professor Osgood demonstrates Fourier transforms of a general distribution.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). In this lecture, Professor Osgood demonstrates Fourier transforms of a general distribution.4331557850Tue, 22 Jul 2008 11:20:49 GMTBrad Osgood0:49:24ScienceStanfordno1314. Fourier Transforms Lecture 14Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on distributions.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on distributions.4331557856Tue, 22 Jul 2008 11:18:09 GMTBrad Osgood0:53:59ScienceStanfordno1415. Fourier Transforms Lecture 15Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood introduces a new application of the Fourier Transforms that includes deltas, properties of deltas, and physical interpretation of deltas.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood introduces a new application of the Fourier Transforms that includes deltas, properties of deltas, and physical interpretation of deltas.4331557862Tue, 22 Jul 2008 11:15:10 GMTBrad Osgood0:52:08ScienceStanfordno1516. Fourier Transforms Lecture 16Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on diffraction and connects it to his next topic, sampling and interpolation.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on diffraction and connects it to his next topic, sampling and interpolation.4331557868Tue, 22 Jul 2008 11:12:19 GMTBrad Osgood0:49:42ScienceStanfordno1617. Fourier Transforms Lecture 17Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood begins his lecture on sampling and interpolation and discusses the associated properties.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood begins his lecture on sampling and interpolation and discusses the associated properties.4331557874Tue, 22 Jul 2008 11:08:08 GMTBrad Osgood0:41:12ScienceStanfordno1718. Fourier Transforms Lecture 18Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues the lecture on sampling and interpolation while discussing some of the phenomenon associated with it.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues the lecture on sampling and interpolation while discussing some of the phenomenon associated with it.4331557880Tue, 22 Jul 2008 11:04:49 GMTBrad Osgood0:51:09ScienceStanfordno1819. Fourier Transforms Lecture 19Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood demonstrates aliasing by showing the class what happens when you under sample music.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood demonstrates aliasing by showing the class what happens when you under sample music.4331557886Tue, 22 Jul 2008 11:02:10 GMTBrad Osgood0:52:05ScienceStanfordno1920. Fourier Transforms Lecture 20Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on the Discrete Fourier Transform.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on the Discrete Fourier Transform.4331557892Tue, 22 Jul 2008 10:58:25 GMTBrad Osgood0:52:52ScienceStanfordno2021. Fourier Transforms Lecture 21Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on the properties of discrete Fourier transforms.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on the properties of discrete Fourier transforms.4331557898Tue, 22 Jul 2008 10:52:59 GMTBrad Osgood0:52:58ScienceStanfordno2122. Fourier Transforms Lecture 22Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on the basics of the fast Fourier transforms algorithm.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on the basics of the fast Fourier transforms algorithm.4331557904Tue, 22 Jul 2008 10:48:56 GMTBrad Osgood0:51:15ScienceStanfordno2223. Fourier Transforms Lecture 23Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on linear systems, focusing on linear time and variance systems.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on linear systems, focusing on linear time and variance systems.4331557910Tue, 22 Jul 2008 10:44:32 GMTBrad Osgood0:51:03ScienceStanfordno2324. Fourier Transforms Lecture 24Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on linear systems.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on linear systems.4331557916Tue, 22 Jul 2008 10:39:56 GMTBrad Osgood0:57:04ScienceStanfordno2425. Fourier Transforms Lecture 25Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on the relationship between LTI and the Fourier transforms.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on the relationship between LTI and the Fourier transforms.4331557922Tue, 22 Jul 2008 10:34:35 GMTBrad Osgood0:53:16ScienceStanfordno2526. Fourier Transforms Lecture 26Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood begins his final topic, space and the higher dimension Fourier Transform.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood begins his final topic, space and the higher dimension Fourier Transform.4331557928Tue, 22 Jul 2008 10:31:13 GMTBrad Osgood0:53:55ScienceStanfordno2627. Fourier Transforms Lecture 27Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his discussion on higher dimensions and the outer reaches while helping the students understand higher dimensions Fourier Transforms.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his discussion on higher dimensions and the outer reaches while helping the students understand higher dimensions Fourier Transforms.4331557934Tue, 22 Jul 2008 10:25:39 GMTBrad Osgood0:49:56ScienceStanfordno2728. Fourier Transforms Lecture 28Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on the higher dimensional Fourier Transforms.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on the higher dimensional Fourier Transforms.4331557940Tue, 22 Jul 2008 10:20:57 GMTBrad Osgood0:49:06ScienceStanfordno2829. Fourier Transforms Lecture 29Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on the general stretch theorem and begins covering medical imaging.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on the general stretch theorem and begins covering medical imaging.4331557946Tue, 22 Jul 2008 10:18:19 GMTBrad Osgood0:50:05ScienceStanfordno2930. Fourier Transforms Lecture 30Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood's last lecture of the quarter, he finishes lecturing on tomography and inverting the radon transform in medical imaging.Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood's last lecture of the quarter, he finishes lecturing on tomography and inverting the radon transform in medical imaging.4331557952Tue, 22 Jul 2008 10:14:11 GMTBrad Osgood0:47:08ScienceStanfordno30