傅里叶变换在数学物理及工程中的应用

Title  Applications of Fourier Transform in Mathematics physics and engineering
Abstract
Fourier Transform is a special integral Transform, which can express a function that meets certain conditions as a linear combination of sinusoidal basis functions or integral form. Since Fourier Transform has many good properties, it has a very wide range of applications in physics, number theory, combinatorics, signal processing, probability, statistics, cryptography, acoustics, optics and other fields. In this paper, which is based on the signal function, it discusses the Fourier Transform, including its history, basic concepts, basic properties, physical meaning in the physical engineering and its application limitations and so on. This paper highlights in signal processing applications, and how to use the Fourier Transform to design filters.
Keywords:  Fourier Transform ; physical application ; signal processing ; filter

1  绪论    1
2  傅里叶变换的发展历史    3
3  傅里叶变换的基本概念    6
3.1  连续傅里叶级数变换    7
3.2  连续傅里叶变换    8
3.3  离散傅里叶级数变换和序列傅里叶变换    9
4  傅里叶变换的基本性质    12
5  傅里叶变换的物理意义    15
6  傅里叶变换在物理工程中的应用    16
6.1  采样    16
6.2  频谱分析    17
6.3  滤波器的设计方法总结    20
7  傅里叶变换应用的局限性    26
7.1  傅里叶变换不具有时间和频率的定位功能    26
7.2  傅里叶变换对于非平稳信号的局限性    26
7.3  傅里叶变换在时间和频率分辨率上的局限性    26

1  绪论

------分隔线----------------------------