30 episodes
The Fourier Transforms and Its Applications Brad Osgood
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- Science
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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- video
1. Fourier Transforms Lecture 1
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood provides an overview of the course, then begins lecturing on Fourier series.
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2. Fourier Transforms Lecture 2
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood's lecture addresses the question- How can we use such simple functions, sin(t) and cos(t) to model such periodic phenomenon? He takes the students through the first steps in analyzing general periodic phenomenon.
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3. Fourier Transforms Lecture 3
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues lecturing on the analysis of periodic phenomena and how it is represented.
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4. Fourier Transforms Lecture 4
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood wraps up the theoretical aspects of the Fourier Series, an application to heat flow.
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5. Fourier Transforms Lecture 5
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood finishes up on Fourier series, then he talks about the transformation Fourier series compared to the Fourier Transform.
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6. Fourier Transforms Lecture 6
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood picks up where he left off last lecture on Fourier Transformations, then he launches into a more formal treatment of Fourier transforms and explains how to proceed.