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Electronics and Communication Signal Processing Difficulty: Medium

Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete-time system has the input-output relationship, $$y\left( n \right) = \left\{ \matrix{ \matrix{ {x\left( n \right),} & {n \ge 1} \cr } \hfill \cr \matrix{ {0,} & {n = 0} \cr } \hfill \cr \matrix{ {x\left( {n + 1} \right),} & {n \le - 1} \cr } \hfill \cr} \right.$$ where x(n) is the input and y(n) is the output. The above system has the properties

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