关于信号tu(t)的傅里叶变换的探讨  

A Discussion about the Fourier Transform of Signal t u(t)

作　　者：宋琪 陆三兰 SONG Qi;LU Sanlan(School of Electronic Information and Communications,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]华中科技大学电子信息与通信学院,武汉430074

出　　处：《电气电子教学学报》2023年第2期120-123,共4页Journal of Electrical and Electronic Education

基　　金：华中科技大学校级教学研究专项项目(2018016);华中科技大学校级研究生教育面上项目(YY202007)。

摘　　要：傅里叶变换是“信号与线性系统”课程中一个非常重要的教学内容,是理解信号频域特性和进行线性系统频域分析的基础。课程中对于一些不满足绝对可积条件的信号,通过引入广义函数获得了它们的傅里叶变换。斜坡信号tu(t)不是绝对可积的信号,虽然一些文献中给出了它的傅里叶变换表达式,但对于该信号的傅里叶变换是否存在的问题却存在不同观点。论文对斜坡信号傅里叶变换的求解方法进行了研究,指出了常见的错误方法,并对斜坡信号的频率特性给出了一种观点。Fourier transform is an important content in the subject of Signals and Linear Systems,as it is the base to understand the frequency characteristic of signals and conduct frequency analysis of linear systems.For some signals which are not absolutely integrable,the Fourier transforms of them are obtained by introducing generalized functions.In some references the Fourier transform of ramp signal t u(t)can be found in the case it is not absolutely integrable,however there are different views about the existence of its Fourier transform.In this paper,methods to obtain the Fourier transform of ramp signal are studied and some wrong methods are indicated,and finally a point of view about the frequency characteristic of ramp signal is provided.

关 键 词：傅里叶变换 广义函数 拉普拉斯变换 

分 类 号：TN911.7[电子电信—通信与信息系统]