《Fourier变换的应用分析》-毕业论文.doc

摘要 以Fourier变换为代表的积分变换在许多工程领域有着广泛应用，因此，总结和分析Fourier变换的主要应用案例，对于加深对积分变换理论和方法的理解有着重要的实际意义。本文首先从Fourier变换的基本理论出发，对其常用性质和Fourier变换的几种重要变种进行了总结。在此基础上，对Fourier变换在一些实际应用中的思想方法以及快速Fourier变换(FFT)的算法实现进行了分析，得出了Fourier变换的一些应用特点。 关键词：Fourier变换，应用分析，仿真模拟 Abstract The integral transformations, e.g., Fourier transformation, have the widespread application in many project domains. Therefore, summarizing and analyzing the Fourier transformation has the highly practical significance to deepen the understanding of the integral transformation theory and method. Begining with the basic theory of Fourier transformation, we summarizes its characters and several kinds of variants. On the basis of these, we further analyze the methods of Fourier transformation via some application examples and the realization of Fast Fourier transformation’s algorithm, and then obtains the festures of Fourier transformation in application. Keywords?:Fourier transform, Application analysis, Simulation 目录 TOC \o 1-2 \h \z \u HYPERLINK \l _Toc199861582 1绪论 PAGEREF _Toc199861582 \h 1 HYPERLINK \l _Toc199861583 1.1 Fourier变换概述 PAGEREF _Toc199861583 \h 1 HYPERLINK \l _Toc199861584 1.2研究目的和意义 PAGEREF _Toc199861584 \h 2 HYPERLINK \l _Toc199861585 2 Fourier变换基本理论 PAGEREF _Toc199861585 \h 3 HYPERLINK \l _Toc199861586 2.1 Fourier级数的定义 PAGEREF _Toc199861586 \h 3 HYPERLINK \l _Toc199861587 2.2 Fourier变换的定义 PAGEREF _Toc199861587 \h 3 HYPERLINK \l _Toc199861588 2.3 Fourier变换的物理意义 PAGEREF _Toc199861588 \h 4 HYPERLINK \l _Toc199861589 2.4 Fourier变换的基本性质 PAGEREF _Toc199861589 \h 5 HYPERLINK \l _Toc199861590 3 Fourier变换几种重要变种 PAGEREF _Toc199861590 \h 8 HYPERLINK \l _Toc199861591 3.1有限长序列的Fourier分析 PAGEREF _Toc199861591 \h 8 HYPERLINK \l _Toc199861592 3.2离散Fourier级数(DFS) PAGEREF _Toc199861592 \h 9 HYPERLINK \l _Toc199861593 3.3离散Fourier变换(DFT) PAGEREF _Toc199861593 \h 10 HYPERLINK \l _Toc199861594 3.4分数阶Fourier变换(FRFT)的定义和性质 PAGEREF _Toc199861594 \h 17 HYPERLINK \l _Toc199861595 4 Fourier变换的应用案例研