冲激函数δ(t)及其导数的微分方程求解

Differential equation solution of impulse function δ(t) and its derivative

线性微分方程的求解是信号与系统课程的核心内容.针对线性微分方程经典求解算法在处理包含冲激函数δ(t)及其一阶、二阶导数甚至高阶导数时,无法解决在0_(-)到0_(+)时刻引起的初始状态变化情况的问题,依据拉氏变换求解微分方程的过程及结果,提出经典求解算法中包含冲激函数δ(t)及其一阶、二阶导数的响应函数形式及系数确定方法.该方法能够快速得到冲激响应的完备表达式,简化了运算过程,弥补了经典微分方程在解决该类问题的不足.

The solution of linear differential equation is the core content of signal and system.Aiming at the problem that the classical solution algorithm of linear differential equation can not solve the change of initial state caused by 0_(-)to 0_(+)time when dealing with the impulse function and its first-order,second-order and even higher-order derivatives,according to the process and results of solving differential equation by Laplace transform,it is proposed that the classical solution algorithm includes impulse function and its first-order Response function form of second derivative and determination method of coefficient.This method can quickly obtain the complete expression of impulse response,simplify the operation process,and make up for the deficiency of classical differential equations in solving this kind of problems.