GATE-2018 (24) :Wyllie – Time average equation

CSIR_NET_JUNE_2019

87) The minimum sampling frequency to record distortion free signal for the function x (t) = Cos (100πt) + Cos (200 πt) is

 

A) 100 Hz 

B) 200Hz 

 C) 50Hz 

D) 400Hz

(Thanks to Chandrasekhar, ANU)

Solution:

The sampling rate is also called as sampling frequency, higher the sample frequency obtains a signal which is similar to original signal for good audio quality

x (t) = Cos (100πt) + Cos (200 πt )----------------------------------------(1)

x (t) = Cos (w₁ t) + Cos (w₂ t) ------------------------------------------(2)

by comparing both the equations 

 

w₁ = 100 π                     w₂ = 200 π

2 πf₁ =100 π                   2 πf₂ =200 π

f₁ = 50 Hz               f₂ = 100 Hz( which is maximum frequency f_max) 

therefore ,

sampling rate is f_s = 2* f_max

                             = 2*100

f_s = 200 Hz