Correct Answer - Option 1 : 7 kHz
Concept:
Nyquist rate is the minimum rate at which a signal can be sampled without introducing errors, which is twice the highest frequency present in the signal.
Nyquist rate = 2 × highest frequency present in the signal
fs = 2fm
Calculation:
\(x\left( t \right) = 2~cos \left( {2000\;\pi t} \right)\cos \left( {5000\;\pi t} \right)\)
\( = \left[ {\cos \left( {3000\;\pi t} \right)+\cos \left( {7000\;\pi t} \right)} \right]\)
ω1 = 3000 π ⇒ f1 = 1500 Hz
ω2 = 7000 π ⇒ f2 = 3500 Hz
fm = max (f1, f2) = 3500 Hz
Nyquist rate, fs = 2fm = 2 × 3500 = 7 kHz
