A linear time-invariant (LTI) system is both a [[linear system]] and a [[time-invariant system]]. It has 3 properties: 1. additivity: $ \begin{array}{c} S(x_1(n)) = y_1(n)\\ S(x_2(n)) = y_2(n)\\ \end{array} \xrightarrow[additivity]{} S(x_1(n) + x_2(n)) = y_1(n) + y_2(n) $ 2. homogeneity: $S(x(n)) = y(n) \xrightarrow[homogeneity]{} S(a x(n)) = a y(n), a \in \mathbb{R}$ 3. time-invariance: $S(x(n)) = y(n) \xrightarrow[time-invariant]{} S(x(n-n_0)) = y(n-n_0)$ If the input signal of the LTI system can be decomposed into a combination of simple signals, the output of the system can be computed as the combination of the system's response to those simple signals.