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

$$y\left [ n \right ]=\underset{-\infty \leq k\leq n}{\text{max}} \mid x\left [ k \right ] \mid$$

The unit impulse response of the system is

  1. $0$ for all $n$.
  2. $1$ for all $n$.
  3. unit step signal $u\left [ n \right ].$
  4. unit impulse signal $\delta \left [ n \right ].$
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