In general, the so-called complete response of a linear, time-invariant filter is given by the superposition of itssignal when the initial state of the filter (all its memory cells) are zeroed to begin with. The initial-condition response is of course the response of the filter to its own initial state, with the input signal being zero. This clean superposition of the zero-state and initial-condition responses only holds in general for linear filters. In §G.3, this superposition will be considered for state-space filter representations.
Decay Response, Initial Conditions Response