EE 261 - The Fourier Transform and its Applications
Stanford Univ. - EE 261 - The Fourier Transform and its Applications. This consists of 30 lectures given
by Professor Brad Osgood. 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.
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. (from see.stanford.edu)
| Lecture 01 - An overview of the course, Periodic Phenomena and the Fourier Series |
| Lecture 02 - Fourier Series; Analyzing General Periodic Phenomenon |
| Lecture 03 - Fourier Series (cont.); Fourier Coefficients |
| Lecture 04 - Fourier Series (cont.); Applications of Fourier Series |
| Lecture 05 - Fourier Series (cont.), Transition from Fourier Series to Fourier Transforms |
| Lecture 06 - Fourier Transform Derivation from Fourier Series, Results of the Derivation |
| Lecture 07 - Review of Fourier Transform (and Inverse) Definitions, Notation, Example |
| Lecture 08 - General Properties of the Fourier Transforms; Convolution |
| Lecture 09 - Example of Convolution: Filtering, Interpreting Convolution in the Time Domain |
| Lecture 10 - Convolution and Central Limit Theorem |
| Lecture 11 - Discussion of the Convergence of Integrals |
| Lecture 12 - Review of Rapidly Decreasing Functions, Generalized Functions (Distributions) |
| Lecture 13 - Fourier Transform of a Distribution, Example of Delta as a Distribution |
| Lecture 14 - Distributions (cont.): Derivative of a Distribution, Example: Derivative of a Unit Step |
| Lecture 15 - Application of the Fourier Transform: Diffraction |
| Lecture 16 - Crystallography Discussion, Fourier Transform of the Shah Function |
| Lecture 17 - Sampling and Interpolation, Discussion of the Associated Properties |
| Lecture 18 - Sampling and Interpolation (cont.) |
| Lecture 19 - Aliasing Demonstration with Music |
| Lecture 20 - Discrete Fourier Transform: Definition, Sample Points, etc |
| Lecture 21 - Properties of Discrete Fourier Transform (cont.) |
| Lecture 22 - The Basics of the Fast Fourier Transforms Algorithm |
| Lecture 23 - Linear Systems: Basic Definitions, Eigenvectors and Eigenvalues |
| Lecture 24 - Linear Systems (cont.): Impulse Response, Linear Time Invariant Systems |
| Lecture 25 - The relationship between LTI Systems and the Fourier Transforms |
| Lecture 26 - The Higher Dimensional Fourier Transform |
| Lecture 27 - Higher Dimensional Fourier Transforms (cont.) |
| Lecture 28 - Higher Dimensional Fourier Transforms (cont.): Shift Theorem, Stretch Theorem |
| Lecture 29 - Shahs, Lattices, and Crystallography |
| Lecture 30 - Tomography and Inverting the Radon Transform |
| Web.. |
EE 261 - The Fourier Transform and its Applications
Instructors: Professor Brad Osgood. Handouts. Assignments. Exams. 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.
see.stanford.edu/see/courseinfo.aspx?coll=84d174c2-d74f-493d-92ae-c3f45c0ee091
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