FFT Algorithm: Setup: DFT Matrix Notation
By Brad G. Osgood - Stanford
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1,105
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Lecture Description
FFT Algorithm: Setup: DFT Matrix Notation, One Intuition Behind FFT: Factoring Matrix, Our Approach: Split Order N Into Two Order N/2, Iterate, Notation (To Keep Track Of Powers Of Complex Exponentials), Plugging New Notation Into DFT; Split Into Even And Odd Indices, Result For Indices 0 To N/2-1, Result For Indices N/2 To N-1, Summary Of Results (DFT As Combination Of 2 Half Order Dfts)
Course Description
Note: This course is being offered this summer by Stanford as an online course for credit. It can be taken individually, or as part of a master’s degree or graduate certificate earned online through the Stanford Center for Professional Development. 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.
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