The Fourier Transforms and Its Applications
By Brad Osgood
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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.
| Name | Description | Released | Price | ||
|---|---|---|---|---|---|
| 1 | Video1. Fourier Transforms Lecture 1 | 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. | 7/22/2008 | Free | View in iTunes |
| 2 | Video2. Fourier Transforms Lecture 2 | 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. | 7/22/2008 | Free | View in iTunes |
| 3 | Video3. Fourier Transforms Lecture 3 | 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. | 7/22/2008 | Free | View in iTunes |
| 4 | Video4. Fourier Transforms Lecture 4 | 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. | 7/22/2008 | Free | View in iTunes |
| 5 | Video5. Fourier Transforms Lecture 5 | 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. | 7/22/2008 | Free | View in iTunes |
| 6 | Video6. Fourier Transforms Lecture 6 | 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. | 7/22/2008 | Free | View in iTunes |
| 7 | Video7. Fourier Transforms Lecture 7 | 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. | 7/22/2008 | Free | View in iTunes |
| 8 | Video8. Fourier Transforms Lecture 8 | 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. | 7/22/2008 | Free | View in iTunes |
| 9 | Video9. Fourier Transforms Lecture 9 | 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. | 7/22/2008 | Free | View in iTunes |
| 10 | Video10. Fourier Transforms Lecture 10 | 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. | 7/22/2008 | Free | View in iTunes |
| 11 | Video11. Fourier Transforms Lecture 11 | 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. | 7/22/2008 | Free | View in iTunes |
| 12 | Video12. Fourier Transforms Lecture 12 | 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. | 7/22/2008 | Free | View in iTunes |
| 13 | Video13. Fourier Transforms Lecture 13 | 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. | 7/22/2008 | Free | View in iTunes |
| 14 | Video14. Fourier Transforms Lecture 14 | 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. | 7/22/2008 | Free | View in iTunes |
| 15 | Video15. Fourier Transforms Lecture 15 | 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. | 7/22/2008 | Free | View in iTunes |
| 16 | Video16. Fourier Transforms Lecture 16 | 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. | 7/22/2008 | Free | View in iTunes |
| 17 | Video17. Fourier Transforms Lecture 17 | 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. | 7/22/2008 | Free | View in iTunes |
| 18 | Video18. Fourier Transforms Lecture 18 | 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. | 7/22/2008 | Free | View in iTunes |
| 19 | Video19. Fourier Transforms Lecture 19 | 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. | 7/22/2008 | Free | View in iTunes |
| 20 | Video20. Fourier Transforms Lecture 20 | 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. | 7/22/2008 | Free | View in iTunes |
| 21 | Video21. Fourier Transforms Lecture 21 | 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. | 7/22/2008 | Free | View in iTunes |
| 22 | Video22. Fourier Transforms Lecture 22 | 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. | 7/22/2008 | Free | View in iTunes |
| 23 | Video23. Fourier Transforms Lecture 23 | 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. | 7/22/2008 | Free | View in iTunes |
| 24 | Video24. Fourier Transforms Lecture 24 | 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. | 7/22/2008 | Free | View in iTunes |
| 25 | Video25. Fourier Transforms Lecture 25 | 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. | 7/22/2008 | Free | View in iTunes |
| 26 | Video26. Fourier Transforms Lecture 26 | 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. | 7/22/2008 | Free | View in iTunes |
| 27 | Video27. Fourier Transforms Lecture 27 | 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. | 7/22/2008 | Free | View in iTunes |
| 28 | Video28. Fourier Transforms Lecture 28 | 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. | 7/22/2008 | Free | View in iTunes |
| 29 | Video29. Fourier Transforms Lecture 29 | 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. | 7/22/2008 | Free | View in iTunes |
| 30 | Video30. Fourier Transforms Lecture 30 | 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. | 7/22/2008 | Free | View in iTunes |
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Customer Reviews
Great Professor
I am enjoying watching your lectures for a pleasure. Prof. Osgood, you are a great professor, math educator, and communicator. I am guessing that you inspired so many generation of students to become mathematicians or engineers. Thank you Stanford University for making this free for those of who seek it. This is a key course to unlock some of the secrets of mathematics that gives so many good stuffs to this world.
Awesome
Very well taught. Very interesting. Thank you.
Pretty amazing
This profession drain me into the subject!! Wow!
