The GATE Grind

GATE 2016 EE – Question 18

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

Consider a continuous-time system with input $x(t)$ and output $y(t)$ given by

$$y(t) = x(t) \cos(t)$$

This system is

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

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Correct answer: (C) linear and time-varying

Explanation

Scaling or adding inputs scales or adds the outputs, so the system is linear. Delaying the input by $t_0$ gives $x(t - t_0)\cos(t)$, but delaying the output gives $x(t - t_0)\cos(t - t_0)$, which is different. So the system is time-varying.