The GATE Grind

GATE 2019 EE – Question 17

Signals and Systems · Linear time invariant and causal systems · 1 mark · Multiple choice

The symbols $a$ and $T$ represent positive quantities, and $u(t)$ is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?

  1. $e^{+at}u(t)$
  2. $e^{-a(t+T)}u(t)$
  3. $1+e^{-at}u(t)$
  4. $e^{-a(t-T)}u(t)$

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Show answer and explanation

Correct answer: (C) $1+e^{-at}u(t)$

Explanation

A causal system has an impulse response that is zero for $t<0$. The term $1$ in option C is non-zero for all $t$, including $t<0$, so it cannot be a causal impulse response. The others are all multiplied by $u(t)$.