| 虚轴上具有重极点的拉普拉斯变换与傅里叶变换相互计算的方法 |
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| 引用本文： | 陈绍荣,何健,朱行涛,刘郁林. 虚轴上具有重极点的拉普拉斯变换与傅里叶变换相互计算的方法[J]. 通信技术, 2020, 0(3): 584-590 |
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| 作者姓名： | 陈绍荣 何健 朱行涛 刘郁林 |
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| 作者单位： | 陆军工程大学通信士官学校;军委装备发展部军事代表局驻成都地区军事代表室;重庆市经信委 |
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| 基金项目： | 重庆高校创新团队建设计划资助(No.KJTD201343)。 |
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| 摘 要： | 提出了一种虚轴上具有重极点的拉普拉斯变换(LT)与傅里叶变换(CTFT)相互计算的方法。对虚轴上具有重极点的LT,通过部分分式展开,将LT在虚轴上的极点分离出来,使其成为虚轴上含极点和不含极点两部分之和,针对虚轴上含极点的LT部分,分区左极点和区右极点两种情况,导出了利用LT计算CTFT的方法;将信号的CTFT分解成解析部分与不解析部分之和,针对CTFT的不解析部分,分因果信号和反因果信号两种情况,导出了利用CTFT计算LT的方法。
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| 关 键 词： | 因果信号 反因果信号 CTFT LT |
Mutual Calculation of Laplace Transform and Fourier Transform with Multiple Poles on Imaginary Axis |
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| CHEN Shao-rong,HE Jian,ZHU Xing-tao,LIU Yu-lin. Mutual Calculation of Laplace Transform and Fourier Transform with Multiple Poles on Imaginary Axis[J]. Communications Technology, 2020, 0(3): 584-590 |
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| Authors: | CHEN Shao-rong HE Jian ZHU Xing-tao LIU Yu-lin |
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| Affiliation: | (Communication Sergeants College,PLA Army Engineering University Chongqing 400035,China;Military Representative Office in Chengdu,Military Representative Bureau of Military Commission Equipment Development Department,Chengdu Sichuan 610041,China;Chongqing Economic and Information Commission,Chongqing 400015,China) |
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| Abstract: | A mutual calculation method of LT(Laplace transform)and CTFT(continuous-time Fourier transform)with multiple poles on imaginary axis is proposed.Firstly,the LT with multiple poles on imaginary axis is separated into the sum of the two parts including the poles on imaginary axis and the poles not on imaginary axis through partial-fraction expansion.Aiming at the LT part with the poles on imaginary axis and via distinguishing the two cases of the left pole and the right pole,the methods for calculating CTFT by using LT are derived;then,based on decomposing CTFT of the signal into the sum of the analytical part and the non-analytical part,aiming at the non-analytical part and via distinguishing two cases of the causal signal and anti-causal signal,the methods for calculating LT by using CTFT also derived. |
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| Keywords: | causal signal anti-causal signal CTFT(continuous-time Fourier transform) LT(Laplace transform) |
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