Question:
A signal \( x(t) = 5 \cos(150\pi t - 60^\circ) \) is sampled at 200 Hz. The fundamental period of the sampled sequence \( x(n) \) is:
A signal \( x(t) = 5 \cos(150\pi t - 60^\circ) \) is sampled at 200 Hz. The fundamental period of the sampled sequence \( x(n) \) is:
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Discrete period = reciprocal of normalized digital frequency \( \frac{f}{f_s} \)
Updated On: May 26, 2025
- \( \frac{1}{200} \)
- \( \frac{2}{200} \)
- 4
- 8
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The Correct Option is D
Solution and Explanation
Continuous frequency:
\[
f = \frac{150\pi}{2\pi} = 75\ \text{Hz}
\]
Sampled at 200 Hz:
Discrete frequency:
\[
f_d = \frac{75}{200} = \frac{3}{8}
\Rightarrow \text{Fundamental period} = \frac{1}{f_d} = 8
\]
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