Derivative of a Distribution
By Brad G. Osgood - Stanford
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Lecture Description
Derivative Of A Distribution, Example: Derivative Of A Unit Step, Example: Derivative Of Sgn(X), Applications To The Fourier Transform (Using The Derivative Theorem), Caveat To Distributions: Multiplying Distributions, Distributions*Functions, Special Case: The Delta Function And Sampling, Convolution In Distributions, Special Case: Convolution When T = Delta, The Scaling Property Of Delta
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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