GATE 2022 IN – Question 16

Communication and Optical Instrumentation · Analog and digital communication · 1 mark · Multiple choice

A sinusoidal carrier with amplitude $A_c$ and frequency $f_c$ is amplitude modulated by $m(t)$ with $0<f_m\ll f_c$, giving $s(t)=A_c[1+m(t)]\cos(2\pi f_ct)$. Which message can be retrieved completely by envelope detection?

$m(t)=0.5\cos(2\pi f_mt)$
$m(t)=1.5\sin(2\pi f_mt)$
$m(t)=2\sin(4\pi f_mt)$
$m(t)=2\cos(4\pi f_mt)$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $m(t)=0.5\cos(2\pi f_mt)$

Explanation

Undistorted envelope detection requires 1+m(t)≥0, so sinusoidal modulation magnitude must not exceed one. Only 0.5cos2πfmt meets that condition; the larger-amplitude choices overmodulate.

Hence **A**.