The GATE Grind

GATE 2020 EC – Question 15

Networks, Signals and Systems · LTI Systems · 1 mark · Multiple choice

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

$$y[n]=\max_{-\infty\le k\le n}|x[k]|.$$

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 $\delta[n]$.

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Show answer and explanation

Correct answer: (C) unit step signal $u[n]$.

Explanation

For $x[n]=\delta[n]$, the running maximum of $|x[k]|$ is $0$ for $n<0$ and becomes $1$ from $n=0$ onwards. So the output is $u[n]$.