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. \( \frac{1}{200} \)
• B. \( \frac{2}{200} \)
• C. 4
• D. 8

Hint:

Discrete period = reciprocal of normalized digital frequency \( \frac{f}{f_s} \)

Answer 1

The Correct Option is D

Continuous frequency: \[ f = \frac{150\pi}{2\pi} = 75\ \text{Hz} \] Sampled at 200 Hz: Discrete frequency: \[ f_d = \frac{75}{200} = \frac{3}{8} \Rightarrow \text{Fundamental period} = \frac{1}{f_d} = 8 \]