The GATE Grind

GATE 2023 EC – Question 27

Communications · Analog Communications · 1 mark · Multiple choice

Let $m(t)$ be a strictly band-limited signal with bandwidth $B$ and energy $E$. Assuming $\omega_0=10B$, the energy in the signal $m(t)\cos\omega_0t$ is

  1. $\dfrac E4$
  2. $\dfrac E2$
  3. $E$
  4. $2E$

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Show answer and explanation

Correct answer: (B) $\dfrac E2$

Explanation

Since $\omega_0\gg B$, the two shifted copies of the spectrum do not overlap. $\cos^2\omega_0t$ averages to $\tfrac12$, so the energy is $E/2$.