How to find the special solution of signal and system zero-state response?

The form of the special solution is determined by the excitation signal, because the pulse signal only works when t=0, that is, Zhit >; , the input signal is 0 or it can be considered that there is no input signal.

However, when t=0, the shock signal changes the installed system, which is no longer zero, so it can be taken as a zero input response. The key is to find the system state when t=0.

Extended data:

The complex frequency domain algebraic equation of the system is constructed, so that the output and its derivative are zero when t=0. The zero-state response of the system is obtained by inverse transformation of the output complex frequency domain function.

The complex frequency domain algebraic equation of the system is constructed, and the output and its derivative are zero. When a first-order circuit with non-zero initial state is excited, the response of the circuit is called the full response of the first-order circuit. For linear circuits, the total response is the sum of zero input response and zero state response.