The Fourier Transforms and its Applications (EE261) Stanford
Online Free Online Course by
World Mentoring Academy
Online
/ Free Online Course
Details
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.
Resources: OpenCourseware from Yale, UC Berkeley, Stanford, MIT along with many of the World's finest University's.
Language: English
Units: 30
Lesson content
- Lec 1 overview & fourier series
- Lec 2 sin(t) and cos(t) to model such periodic phenomenon?
- Lec 3 analysis of periodic phenomena
- Lec 4 theoretical aspects of the Fourier Series, an application to heat flow
- Lec 5 periodic phenomena to non periodic phenomena by means of a limiting process.
- Lec 6 formal treatment of Fourier transforms
- Lec 7 Fourier Transform and its inverse
- Lec 8 convolutions, delays, stretches
- Lec 9 convolution & signal combinations
- Lec 10 central limit theorem
- Lec 11 confronting the convergence of intervals
- Lec 12 rapidly decreasing functions.
- Lec 13 Fourier transforms of a general distribution.
- Lec 14 distributions
- Lec 15 Deltas
- Lec 16 diffraction, sampling and interpolation
- Lec 17 sampling, interpolation and associated properties
- Lec 18 sampling and interpolation
- Lec 19 aliasing
- Lec 20 Discrete Fourier Transform
- Lec 21 properties of discrete Fourier transforms
- Lec 22 Fourier transforms algorithm
- Lec 23 linear systems, linear time and variance systems
- Lec 24 linear systems
- Lec 25 relationship between LTI and the Fourier transforms
- Lec 26 space and the higher dimension Fourier Transform
- Lec 27 higher dimensions and the outer reaches
- Lec 28 higher dimensional Fourier Transforms
- Lec 29 general stretch theorem and medical imaging
- Lec 30 tomography and inverting the radon transform in medical imaging.
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World Mentoring Academy is offering FREE Open Courseware. Setup a free user account & select courses with video lectures, Syllabus, Free textbooks when avail., assignments/homework, testing from MIT, Harvard, UC Berkeley, Stanford, U of Mich, Yale along with many of the World's finest University's (700+courses/24-48+ Lectures)
