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課程簡介:

Course Coordinator: Brad Osgood

Course Description: The Fourier transform is ubiquitous in engineering and science and this course is appropriate for students from across the engineering and science disciplines.

The course emphasizes both mathematical know-how and applications.

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.

目錄:


課程內容預覽:

Topics include:
1. Periodicity and Fourier series
2. The Fourier transform and its basic properties
3. Convolution and its applications
4. Distributions and their Fourier transforms
5. Sampling and interpolation
6. Linear systems
7. The discrete Fourier transform
8. Higher dimensional Fourier transforms and applications