傅里叶变换,总结.docVIP

傅里叶变换,总结 解析傅里叶变换 本科毕业论文（设计） 题目 解析傅里叶变换 2013 年4 月 30日 解析傅里叶变换 西南大学电子信息工程学院，重庆 400715 摘要：傅里叶变换的实质就是将信号分解成不同频率复指数信号的叠加，由于复指数信号在LTI系统中的响应十分简单，且傅里叶变换具有多种极其有用的性质使得傅里叶变换在信号分析中得以广泛运用。信号的傅里叶变换有多种形式，且各种变换间具有很强联系：如非周期信号的周期性扩展，其傅里叶级数是原信号傅里叶变换的等间隔采样；若离散序列由连续信号周期取样得到，则离散序列的DTFT是连续信号FT以取样频率进行周期性扩展后的尺度变换。为了用计算机对信号进行傅里叶分析，而引入DFT，它是对信号时域和频域的采样。各种FFT算法的提出大大减少了DFT的运算次数，使DFT得以广泛应用，并极大促进了数字信号处理技术的发展。 关键字：LTI系统；卷积；傅里叶变换；DFT Analysis of Fourier Transform LIU Chaoyuan School of Electronic and Information Engineering, Southwest China University, Chongqing 400715, China Abstract: The essence of the Fourier transform to signal is decomposed into different frequency of complex exponential signals, due to the response of complex exponential signals in LTI system is very simple, and the Fourier transform has many useful properties make Fourier transform can be widely used in signal analysis. Signal Fourier transform has many forms, and has a strong link between each other: such as periodic extension of non-periodic signal, the Fourier series(FS) is the original signal Fourier transform(FT) interval sampling; if the discrete sequence obtained by continuous signal sampling, discrete sequence of DTFT is the scale transform of the continuous signal FT periodic extension by the sampling frequency. In order to use the computer to Fourier analysis of the signal, then introduction the DFT, which is the sampling of the signal in time domain and frequency domain. A Variety of FFT algorithms proposed greatly reducing the number of DFT calculations, so DFT can be widely used, and greatly promote the development of digital signal processing technology. Key words: LTI systems;Convolution;Fourier Transform;DFT 目录 第一章 引言 ..................................................................................................................................... 1 1.1 历史背景 ........................................................................................................................... 1 1.2 本文所研究内容 ...........