“非有理真分式”情况下拉普拉斯逆变换方法探究

Research on Inverse Laplace Transform in the Case of"Non Rational Proper Fraction"

《:信号与系统》课程是电子信息等多个专业的必修课程,该课程主要讲解傅里叶变换、拉普拉斯变换和Z变换这三大经典变换的相关知识。本文通过对该课程中非有理真分式“分子分母同次”情况下,利用传统的多项式长除法求解拉普拉斯逆变换的分析,对比提出另一种新的快捷求解方法,该方法可省略“传统的先利用多项式长除法,将非有理真分式化成有理真分式”的环节,直接进行部分分式展开法求解逆变换。

Signals and systems is a compulsory course for many majors such as electronic information,this course mainly introduces the knowledge of Fourier transform,Laplace transform and Z transform.In this paper we use the method of"the same numerator and denominator"in the course,the traditional long division method is used to solve the inverse Laplace transform,contrast and propose another new quick solution method,this method can omit the link of"transforming non rational true fraction into rational true fraction by using polynomial long division",direct partial fraction expansion method to solve the inverse transformation.