文档介绍：论文编码:
首都师范大学本科学生毕业论文
傅里叶变换的可视化及应用研究
作者: 吴晓龙
院系: 物理系
专业: 物理学(师范)
学号: 1070600080
指导教师: 郭怀明
日期: 2011年5月9日
中文提要
傅里叶变换是由实空间向频谱空间的变换。傅里叶变换的重要性在于很多实际问题在频谱空间更易处理,而快速傅里叶变换的发展则使之更便于应用。本文涉及傅里叶级数、连续傅里叶变换、快速傅里叶变换、广义傅里叶级数,旨在介绍它们之间的区别与联系,并探讨它们在MatLab中的可视化实现方法,以及在实际中的应用。本文最后还对傅里叶变换的意义做了简单探讨。
关键词:傅里叶级数傅里叶变换快速傅里叶变换可视化
Abstract
Fourier Transform is a kind of transformation from the real-space to frequency-space. The reason why Fourier Transform is important is that many realistic problems are more easily to be solved in frequency-space. Specially,the development of Fast Fourier Transform make it more convenient to use. This paper reviews Fourier Series,Fourier Transform, Fast Fourier Transform and Generalized Fourier Series. We discuss the relationship and the difference among them,and introduce their applications in realistic problems,then visualize them in MatLab. Finally,we make ments on the meaning of Fourier Transform.
Keywords:Fourier Series Fourier Transform FFT Visualization
目录
一、引言····································································1
二、傅里叶级数、傅里叶变换的可视化及应用····································1
傅里叶级数、傅里叶变换的数学依据····································1
、傅里叶变换的Matlab可视化实现···························2
、傅里叶变换的实际应用····································3
三、DFT、FFT的可视化及应用··················································4
DFT、FFT的数学依据··················································4
FFT的Matlab可视化实现··············································5
FFT的实际应用·······················································6
四、广义傅里叶级数的可视化及应用············································8
广义傅里叶级数的数学依据············································8
广义傅里叶级数的Matlab可视化实现
···································9
广义傅里叶级数的实际应用············································9
五、傅里叶级数、傅里叶变换的意义···········································11
六、总结及结论·····························································12
附录···················