The GATE Grind

GATE 2022 EE – Question 48

Signals and Systems · Linear time invariant and causal systems · 2 marks · Multiple choice

Consider the system as shown below

where $y(t)=x(e^t)$. The system is

  1. linear and causal.
  2. linear and non-causal.
  3. non-linear and causal.
  4. non-linear and non-causal.

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Show answer and explanation

Correct answer: (B) linear and non-causal.

Explanation

The system is linear since a scaled sum of inputs gives the same scaled sum of outputs. It is non-causal because, for $t>0$, $e^t>t$, so the output at time $t$ depends on the future input $x(e^t)$ (for example $y(0)=x(1)$).