Question

For the signal \( x(t) = [1 + 0.5 \cos(40\pi t)] \cos(200\pi t) \), find the fundamental frequency in Hz.

• A. 20
• B. 40
• C. 100
• D. 200

Hint:

Fundamental frequency = LCM of all component frequencies.

Answer 1

The Correct Option is A

Signal is AM (Amplitude Modulated): Carrier freq \( f_c = 100 \), modulating freq \( f_m = 20 \). Fundamental period is LCM of their periods → LCM of \( \frac{1}{100} \) and \( \frac{1}{20} \) = \( \frac{1}{20} \) \[ f_0 = \frac{1}{T_0} = 20\ \text{Hz} \]