The output y[n] of a discrete-time system for an input x[n] is

\(y\left[ n \right] = \mathop {\max }\limits_{ - \infty \le k \le n} \left| {x\left[ k \right]} \right|\)

The unit impulse response of the system is

1
0 for all n
2
1 for all n
3
unit step signal u[n]
4
unit impulse signal δ[n]

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