The GATE Grind

GATE 2023 EC – Question 26

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

Consider a system with input $x(t)$ and output $y(t)=x(e^t)$. The system is

  1. Causal and time invariant.
  2. Non-causal and time varying.
  3. Causal and time varying.
  4. Non-causal and time invariant.

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Show answer and explanation

Correct answer: (B) Non-causal and time varying.

Explanation

Causality: $y(t)$ depends on $x$ at $e^t$, and $e^t>t$ for all real $t$, so the output at time $t$ depends on a future input value: non-causal. Time invariance: delaying the input by $t_0$ gives $x(e^t-t_0)$, while delaying the output gives $x(e^{t-t_0})$; these are different, so the system is time varying.