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

The given signal is \( x(t) = [1 + 0.5 \cos(40\pi t)] \cos(200\pi t) \). To find the fundamental frequency of this signal, analyze its components.

The signal consists of two frequencies:

• The term \( \cos(40\pi t) \) has a frequency of \( \frac{40\pi}{2\pi} = 20 \) Hz.
• The term \( \cos(200\pi t) \) has a frequency of \( \frac{200\pi}{2\pi} = 100 \) Hz.

To determine the fundamental frequency, consider the lowest frequency component. Here, the fundamental frequency is determined by the lowest frequency, which is 20 Hz, corresponding to the \( \cos(40\pi t) \) component.

Thus, the fundamental frequency of the signal is 20 Hz.