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


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

Correct Answer: a) 300Hz


For the given signal,

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

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

Nyquist rate = 2 fmax

= 2* 150

= 300Hz.
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