快速傅里叶变换原理及其应用(快速入门)

快速傅里叶变换的原理及其应用

摘要

快速傅氏变换（FFT），是离散傅氏变换的快速算法，它是根据离散傅氏变换的奇、偶、虚、实等特性，对离散傅立叶变换的算法进行改进获得的。它对傅氏变换的理论并没有新的发现，但是对于在计算机系统或者说数字系统中应用离散傅立叶变换，可以说是进了一大步。傅里叶变换的理论与方法在“数理方程”、“线性系统分析”、“信号处理、仿真”等很多学科领域都有着广泛应用,由于计算机只能处理有限长度的离散的序列,所以真正在计算机上运算的是一种离散傅里叶变换. 虽然傅里叶运算在各方面计算中有着重要的作用，但是它的计算过于复杂，大量的计算对于系统的运算负担过于庞大，使得一些对于耗电量少，运算速度慢的系统对其敬而远之，然而，快速傅里叶变换的产生，使得傅里叶变换大为简化，在不牺牲耗电量的条件下提高了系统的运算速度，增强了系统的综合能力，提高了运算速度，因此快速傅里叶变换在生产和生活中都有着非常重要的作用，对于学习掌握都有着非常大的意义。

关键词快速傅氏变换；快速算法；简化；广泛应用

Abstract

Fast Fourier Transform (FFT), is a discrete fast Fourier transform algorithm, which is based on the Discrete Fourier Transform of odd and even, false, false, and other characteristics of the Discrete Fourier Transform algorithms improvements obtained. Its Fourier transform theory has not found a new, but in the computer system or the application of digital systems Discrete Fourier Transform can be said to be a big step into. Fourier transform theory and methods in the "mathematical equation" and "linear systems analysis" and "signal processing, simulation," and many other areas have a wide range of applications, as the computer can only handle a limited length of the sequence of discrete, so true On the computer's operation is a discrete Fourier transform. Fourier Although all aspects of computing in the calculation has an important role, but its calculation was too complicated, a lot of computing system for calculating the burden is too large for some Less power consumption, the slow speed of operation of its system at arm's length, however, have the fast Fourier transform, Fourier transform greatly simplifying the making, not in power at the expense of the conditions to increase the speed of computing systems, and enhance the system The comprehensive ability to improve the speed of operation, the Fast Fourier Transform in the production and life have a very important role in learning to master all have great significance.

Key words Fast Fourier Transform; fast algorithm; simplified; widely used

目录

摘要………………………………………………………………………………１ABSTRACT………………………………………………………………………２

绪论………………………………………………………………………………４快速傅里叶变换原理……………………………………………………………５快速傅里叶的实际应用…………………………………………………………７１快速傅里叶变换在喇曼光谱信号噪声平滑中的应用…………………７

引言………………………………………………………………………７

实验原理及结果…………………………………………………………８

结论………………………………………………………………………９２采用异步实现的快速傅里叶变换处理器………………………………９引言……………………………………………………………………９

实验原理及结果………………………………………………………１０

结论……………………………………………………………………１０３快速傅里叶算法在哈特曼夏克传感器波前重构算法中的应用………１１引言……………………………………………………………………１１

实验原理及结果………………………………………………………１１

结论……………………………………………………………………１２参考文献…………………………………………………………………………１３