Please answerSolutionThe Cutoff Frequency of ideal Low pass

Please answer

The Cutoff Frequency of ideal Low pass filter is given as wc=2000*pi

i.e Fc=wc/2*pi=2000*pi/(2*pi)=1000 Hz

It means the signals having frequency greater than 1000 Hz is eliminated in the output

The maximum frequency that can be present at the output is Fc=1000 Hz

As per sampling theorem the sampling frequency should be atleast twice the frequency of the signal

so sampling frequency Fs>2*Fc=2000 Hz so Fs>2000 Hz

Looking at the options

(a) Ts=10^-4 and Fs=1/Ts=10000 Hz > 2000 Hz so it can guarantee that x(t) can be recovered

(b) Ts=0.25*10^-3 and Fs=1/Ts=4000 Hz > 2000 Hz so it can guarantee that x(t) can be recovered