时域下初始状态转换为激励

在信号与系统教科书中一般认为，复变换域中利用单边z变换或单边拉氏变换可以求解系统的零输入响应和零状态响应，而时域中的卷积运算只能求零状态响应。这是不全面的。本文通过在时域下将系统初始状态转换为激励信号，从而使得利用卷积运算不仅能够计算零状态响应而且可以求解完全响应和零输入响应。它使得时域分析更全面，丰富了时域分析的内容。也使得学生更好的理解时域分析的核心是卷积运算。

Convert Initial-State into Excitation in Time Domain

In the textbooks for signals and system, it is well known that single-sided z-transform or singlesided Laplace transform in complex frequency-domain may be applied to calculating zero-input response and zero-state response, but convolution operation can only be applied to calculating zero-state response. So it is unilateral. By converting initial-state into excitation in time domain, the complete response and zero-input response may also be calculated using convolution operation. It will enrich the content of time domain analysis. Students can well understand that the kernel of time domain analysis is convolution operation.