The GATE Grind

GATE 2018 EC – Question 38

Communications · Random Processes · 2 marks · Multiple choice

Consider a white Gaussian noise process $N(t)$ with two-sided power spectral density $S_N(f)=0.5$ W/Hz as input to a filter with impulse response $0.5e^{-t^2/2}$ (where $t$ is in seconds) resulting in output $Y(t)$. The power in $Y(t)$ in watts is

  1. 0.11
  2. 0.22
  3. 0.33
  4. 0.44

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Correct answer: (B) 0.22

Explanation

The output power is $S_N\int|h(t)|^2dt=0.5\times\int0.25e^{-t^2}dt=0.125\sqrt\pi=0.2216\approx0.22$ W, using Parseval's theorem.