Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete-time system has the input-output relationship,
\[y\left( n \right) = \left\{ {\begin{array}{*{20}{c}} {x\left( n \right),}&{n \geqslant 1} \\ {0,}&{n = 0} \\ {x\left( {n + 1} \right)}&{n \leqslant - 1} \end{array}} \right.\]
Where x(n) is the input and y(n) is the output.
The above system has the properties