利用DFT在分析信号调制时频率泄漏的讨论  

Discussion on Leakage of Windowing the Modulated Signal Using DFT

作　　者：刘留[1] 胡健[1] 李艳凤[1] 薛健[1] 陈后金[1] LIU Liu;HU Jian;LI Yan-feng;XUE Jian;CHEN Hou-jin(School of Electronic and Information Engineering,Beijing Jiaotong University,Beijing 100044,China)

机构地区：[1]北京交通大学电子信息工程学院,北京100044

出　　处：《教育教学论坛》2020年第21期116-117,共2页Education And Teaching Forum

基　　金：2019年北京市教育委员会“北京市共建—教学名师、青年名师”(351363535);2017年北京交通大学教师发展中心“信号处理系列课程虚拟教研室建设”(356037535)。

摘　　要：窗函数在分析信号频谱中具有重要的作用,文章以利用DFT分析信号调制频谱为例,研究时域加窗截断对调制信号的频率泄漏问题,证明了矩形窗函数频谱函数和矩形窗频谱函数的卷积仍为矩形窗函数的频谱函数。说明对调制信号频谱分析中,相乘后加窗和加窗后相乘,截断的调制信号频谱函数相同,频域上仅存在"一次"泄漏,最后利用仿真实验证明了这一结论,有利于对于时域加窗问题教师教学和学生理解。Time windowing has important significance in theory and practice for digital signal processing.In this paper,the leakage of windowing the modulated signal using DFT is investigated.We prove that the convolution result of frequency functions of two rectangular windows is the frequency function of a rectangular window.By using this result,we can get that the frequency functions of the two time windowing methods(multiplying before windowing and windowing before multiplying)are the same.This means that there is only one leakage caused by the time windowing modulated signal.The result is beneficial to understanding the time windowing problems.

关 键 词：窗函数 频谱分析 加权的矩形窗 

分 类 号：TN911.72[电子电信—通信与信息系统]