Question

A continuous system is described by \( y(t) = x(t) \cos(200 \pi t) \). If \( x(t) \) is a two-tone signal with frequencies 25 Hz and 50 Hz, then the frequency components present in \( y(t) \) will be

• A. 25 Hz and 50 Hz
• B. 100 Hz
• C. 50 Hz, 75 Hz, 125 Hz and 150 Hz
• D. 25 Hz, 50 Hz, 75 Hz and 150 Hz

Hint:

Use trigonometric identities to analyze frequency components in modulated signals.

Answer 1

The Correct Option is D

- Given \( x(t) \) contains frequencies 25 Hz and 50 Hz, multiplying by a cosine function introduces sum and difference frequency components. - The resulting frequencies are 25 Hz, 50 Hz, 75 Hz, and 150 Hz.
Conclusion: The correct frequency components are given by option (d).