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任何一个线性时不变离散系统的输入输出关系都可用线性差分方程式来描写。差分方程式的解答包括两部分:即自由分量和强制分量。它也可以分解成零输入分量和零状态分量。在求全解时,自由分量和零输入分量都是差分方程式的齐次解,二者具有相同形式,但其物理意义却不同。自由分量为有起因序列,零输入分量为无起因序列。这一点对正确地利用初始条件求解差分方程式是非常重要的。本文主要说明二者的差别,并用简单例子说明如何决定二者所含有的常数的方法。
The input-output relationship of any linear time-invariant discrete system can be described by a linear difference equation. The solution to the difference equation consists of two parts: the free component and the forcing component. It can also be decomposed into zero-input components and zero-state components. In seeking solutions, both free and zero input components are homogeneous solutions of difference equations, both of which have the same form but have different physical meanings. The free component is the cause sequence, and the zero input component is the non-cause sequence. This is very important for solving the difference equation correctly using the initial conditions. This article focuses on the differences between the two and uses simple examples to illustrate how to determine the constants contained in both.