关于LTI系统零点跳变问题的研究

Research on the Problem of Initial State Change in LTI System

在确定性输入信号作用下的集总参数线性时不变系统简称LTI系统,包括连续时间系统与离散时间系统。在连续时间系统分析中,由于激励信号的加入,系统状态在零时刻可能发生跳变,从而无法利用原有的起始储能确定系统响应的初值,为系统分析增加了难度。针对于此,文中提出了解决零点跳变的两种方法:冲激函数匹配法与拉普拉斯变换法。从时域、频域角度,通过实例验证讨论了两种方法各自的特点,对理解信号与系统理论的基本概念与分析方法有一定帮助。

Under the action of deterministic input signals,the lumped parameter linear time-invariant system is called LTI system for short,which includes continuous-time system and discrete-time system.In the continuous time system analysis, the system state may change at the initial moment because of the excitation signal.We can not use the original starting storage to determine the initial value of the system response,which adds difficulty to the system analysis.Two methods are proposed to solve the problem：Impulse function matching method and method of Laplace transform. The characteristics of the two methods are described by examples from time domain and frequency domain.It helps us to understand the basic concepts and analysis methods of signal and system theory.