Lectures (Video)
- 1. The Fourier Series
- 2. Periodicity, Modeling A Signal
- 3. Convergence
- 4. Inner Product, Complex Exponentials
- 5. Fourier Transforms
- 6. Fourier Inversion
- 7. Duality Property
- 8. Stretch Theorem Formula, Convolution Formula
- 9. Continuing Convolution
- 10. Central Limit Theorem And Convolution
- 11. Best Class Of Signals For Fourier Transforms
- 12. Generalized Functions
- 13. Fourier Transform Of A Distribution
- 14. The Delta Function And Sampling
- 15. Application Of The Fourier Transform
- 16. Shah Function, Poisson Summation Formula
- 17. Interpolation Problem
- 18. Sampling Rate, Nyquist Rate, Aliasing
- 19. Discrete Version Of The Fourier Transform
- 20. Discrete Complex Exponential Vector
- 21. Review Of Basic DFT Definitions
- 22. FFT Algorithm
- 23. Linear Systems
- 24. Impulse Response, Schwarz Kernel Theorem
- 25. Fourier Transform For LTI Systems
- 26. Higher Dimensional Fourier Transform
- 27. Fourier Transforms Of Seperable Functions
- 28. Shift Theorem
- 29. Shahs, Lattices, And Crystallography
- 30. Tomography And Inverting The Radon Transform
Fourier Transform and its Applications - Lecture 13
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Lecture 13 - Fourier Transform Of A Distribution
Setting Up The Fourier Transform Of A Distribution, Example Of Delta As A Distribution, Distributions Induced By Functions (Includes Many Functions), The Fourier Transform Of A Distribution, The Class Of Tempered Distributions, FT Of A Tempered Distribution, Definition Of The Fourier Transform (By How It Operates On A Test Function), The Inverse Fourier Transform (Proof), Calculations Of Fourier Transforms Using This Definition (Distributions)
Prof. Brad G Osgood
The Fourier Transform and its Applications EE261 (Stanford University: Stanford Engineering Everywhere) http://see.stanford.edu Date accessed: 2009-09-24 License: Creative Commons Attribution 3.0 |
