Complete Response

The complete response of a linear system consists of the superposition of (1) its response to the input signal $\underline{u}(n)$ and (2) its response to initial conditions ${\underline{x}}(0)$:

$$\underline{y}(n) = \underline{y}_u(n) + \underline{y}_x(n),$$

where $\underline{y}_u(n)$ was defined in Eq. (E.3) and $\underline{y}_x(n)$ was defined in Eq. (E.4) above.