摘要数字信号处理作为一种先进的信号处理的手段，在工业、能源、医疗等领域都有广 泛的应用。它的主要研究方向有信号时域和频谱的分析以及滤波器设计。精确的幅值测 量在频谱分析中是非常关键的。FFT(快速傅里叶变换)中能量的泄漏和产生的栅栏效应可 能会导致在频率特性计算和频谱分析时产生相对来说很大的误差。为了减小在峰值估计 时产生的误差，同时也尽可能的提高估计精度，本文主要研究了双窗法，即采用矩形窗 和改进后的窗函数共同作用来进行频谱分析，并通过MATLAB进行了仿真。根据仿真结 果可以得出这种方法一定程度上减小了幅值估计误差，但也有其不足之处，并且提出了 改进方案。76104

毕业论文关键词数字信号处理快速傅里叶变换频谱分析误差双窗法

毕 业 设 计 说 明 书 外 文 摘 要

TitleStudy on reducing the estimation errors of FFT spectrum with dual window method

Abstract As an advanced means for signal processing, digital signal processing have a wide range of applications in industry, energy, medical and other fields。 It has its main research areas in analysis of signal in time and frequency domain and filter design。 Accurate measurement of amplitude is crucial in the spectrum analysis。 In FFT (Fast Fourier Transform), energy leakage and picket-fence effect may result in relatively large errors in the calculations of frequency characteristics and spectrum analysis。 In order to reduce the error in the estimation of peak generation, but also to improve the estimation accuracy as much as possible, this paper mainly focuses on dual window method。 It is a method which uses a rectangular window function along with an improved window for spectral analysis, and verified by MATLAB simulation。 According to the simulation results, we can come to the conclusion that the dual window method reduces the estimation error of magnitude to some extent, but it also has some drawbacks, and an improved proposal is presented。

Keywords Digital signal processing, fast Fourier transform, spectrum analysis error, dual window method

目次

1引言·······1

1。1数字信号处理简介 ····1

1。2频谱分析的研究与发展 ····1

1。3主要内容和工作 ····2

2FFT 算法的基本原理 ······3

2。1离散傅里叶变换的算法和复杂性3

2。2FFT 算法的提出和 MATLAB 实现3

3FFT 算法的频谱误差分析 ······6

3。1连续信号的频谱计算 ····6

3。2连续信号的频谱分析 ····6

3。3能量泄漏与栅栏效应的关系 ····8

4窗函数的功能与介绍 ······9

4。1相关原理9

4。2常用的窗函数 ····9

4。3恢复系数的引入 ·····13

5双窗法的实现与仿真 ····14

5。1双窗法的基本原理 ·····14

5。2双窗法的应用与仿真 ·····17

6双窗法的分析与改进 ····21

6。1仿真结果的分析与讨论 ·····21

6。2研究与改进 ·····21

结 论········24

致 谢········25

参 考 文 献26