The GATE Grind

GATE 2021 EE – Question 16

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

If the input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\max(0,x(t))$, then the system is

  1. linear and time-variant
  2. linear and time-invariant
  3. non-linear and time-variant
  4. non-linear and time-invariant

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Correct answer: (D) non-linear and time-invariant

Explanation

The max operation violates superposition (for example $x=-1$ gives $0$ but $x=1$ gives $1$, so $y(-x)\ne-y(x)$), so the system is non-linear. The rule does not depend on $t$, so a shifted input gives a shifted output, and it is time-invariant.