A system with input $$x\left( n \right)$$ and output $$y\left( n \right)$$ is given as $$y\left( n \right)$$ $$ = \left( {\sin {5 \over 6}\,\pi \,n} \right)x\left( n \right).$$ The system is

The impulse response $$h\left[ n \right]$$ of a linear time invariant system is given as
$$h\left[ n \right] = \left\{ {\matrix{ { - 2\sqrt 2 ,} & {n = 1, - 1} \cr {4\sqrt 2 ,} & {n = 2, - 2} \cr {0,} & {otherwise} \cr } } \right.$$

If the input to the above system is the sequence $${e^{j\pi n/4}},$$ then the output is

A causal LTI system is described by the difference equation $$2y\left[ n \right] = ay\left[ {n - 2} \right] - 2x\left[ n \right] + \beta x\left[ {n - 1} \right].$$ The system is stable only if

Let P be linearity, Q be time-invariance, R be causality and S be stability.

A discrete time system has the input-output relationship,

$$y\left( n \right) = \left\{ {\matrix{ {x\left( n \right),} & {n \ge 1} \cr {0,} & {n = 0} \cr {x\left( {n + 1} \right),} & {n \le - 1} \cr } } \right.$$

Where $$x\left( n \right)\,$$ is the input and $$y\left( n \right)\,$$ is the output. The above system has the properties