斯坦福大学开放课程：傅立叶变换及应用，斯坦福大学以其卓越的开放课程而闻名，其中一门课程深入探讨了傅立叶变换及其应用，傅立叶变换是一种数学工具，能够将信号从时域转换到频域，揭示信号的频率成分，这门课程不仅详细解释了傅立叶变换的基本原理，还探讨了其在信号处理、图像分析、音频编辑等多个领域的应用，通过学习这门课程，学生可以深入了解傅立叶变换的精髓，掌握其在实际问题中的应用技巧。
中文名: 开设斯坦福大学课程 : 傅立叶变换及应用
英文名: Open Stanford Course : The Fourier Transform and Its Applications
资源格式: MP4
课程类型: 数学
学校: Stanford University
斯坦福大学主讲人： Brad Osgood版： 开放式课程 更新完毕
发行日期: 2009年
地区: 美国
对白语言: 英语
文字语言: 英文
课程简介:
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.
目录:
课程内容预览：
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
