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 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
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Use trigonometric identities to analyze frequency components in modulated signals.
Updated On: June 02, 2025
- 25 Hz and 50 Hz
- 100 Hz
- 50 Hz, 75 Hz, 125 Hz and 150 Hz
- 25 Hz, 50 Hz, 75 Hz and 150 Hz
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The Correct Option is D
Solution and Explanation
- 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).
Conclusion: The correct frequency components are given by option (d).
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