Linear Systems and Optimization |
The Fourier Transform and its Applications
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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.
Brad G Osgood
Osgood is a mathematician by training and applies techniques from analysis and geometry to various engineering problems. He is interested in problems in imaging, pattern recognition, and signal processing.
Complete Course Material Downloads:Course Handouts: The ZIP file below contains all of the course handouts for this course. If you do not need the complete course, individual documents can be downloaded from the course content pages.
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