For a continuous time signal x(t) = 8 cos 200 ∏t.
Find: (1) Minimum sampling rate. (2) If f_s= 400Hz,what is discrete time signal? (3) If f_s= 150Hz,what is discrete time signal? (4) Comment on result obtained in 2 and 3 with proper justification.

Subject : Signals & Systems

Topic : Continuous Time Fourier Transform (CTFT) and Discrete Time Fourier Transform (DTFT).

Difficulty: Medium

(1) w_m= 200π 2 πF_m = 200 π F_m= 200π/2π = 100
∴ Minimum sampling rate (F_s) = 2F_m = 200Hz

(2) If F_s = 400Hz, then T = 1/F_s = 1/400. Since, x(t) = 8 cos200 πt
∴ put t = nT for discrete time signal x(nT) = 8 …