关于信号傅里叶变换存在条件问题的探讨  

Discussion about the Existence Condition of Signal Fourier Transform

作　　者：王道宪[1] 段晓辉[1] 杨光临[1] 

机构地区：[1]北京大学信息科学技术学院,北京100871

出　　处：《电子与信息学报》2013年第11期2790-2794,共5页Journal of Electronics & Information Technology

基　　金：国家高技术研究发展计划(2011AA01A106)资助课题

摘　　要：对于一个任意给定的信号,判断其傅里叶变换是否存在一直是尚未解决的问题。由于此问题在信号分析类课程的教学或工程应用中常给人们带来困扰,该文对此进行了分析。从质疑斜坡信号的傅里叶变换入手,通过与常见能量信号和功率信号的傅里叶变换特征相对比,指出了斜坡信号傅里叶变换的一些问题。分析表明斜坡信号不满足傅里叶积分定理,并据此认为斜坡信号的傅里叶变换不成立。最后,通过仿真分析对所持观点进行了验证,并对一些常见信号傅里叶变换的一般规律进行了归纳总结。For any given signal, determining the existence of its Fourier transform has remained an unsolved problem. This raises many concerns in the teaching of signal analysis courses, and also in many engineering applications. This paper presents an analysis of the problem. By comparing the characteristics of the ramp signal,s Fourier transform with that of the Fourier transforms of common energy signals and power signals, the author points out some problems regarding the Fourier transform of the ramp signal. This analysis shows that ramp signal does not satisfy the Fourier integral theorem, thus invalidating the Fourier transformation of ramp signal. Finally, the author further proves this assertion through simulation analysis, and summarizes the general rules of some common signal,s Fourier transform.

关 键 词：信号分析 傅里叶变换 频谱 

分 类 号：TN911.6[电子电信—通信与信息系统]