Numerical - Calculation of Nyquist rate for sampling

Calculate the Nyquist rate for sampling when a continuous time signal is given by
x(t) = 5 cos 100πt +10 cos 200πt -15 cos 300πt

Options:

a) 300Hz
b) 600Hz
c) 150Hz
d) 200Hz

Correct Answer: a) 300Hz

Explanation:

For the given signal,

f₁ = 100π/2π = 50Hz
f₂ = 200π/2π = 100Hz
f₃= 300π/2π = 150Hz

The highest frequency is 150Hz. Therefore f_max= 150Hz

Nyquist rate = 2 f_max

= 2* 150

= 300Hz.