Correct Answer - Option 3 :
\(\frac{1}{{700}}sec\)
Concept:
Nyquist rate: The minimum sampling rate is often called the Nyquist rate. The Nyquist sampling rate is two times the highest frequency of the input or message signal.
\({\rm{\;}}{f_s} = 2{f_m}\)
Where,
fs is the minimum sampling frequency or Nyquist rate
fm is the highest frequency of the input or message signal.
Calculation:
sinc(700t) + sinc(500t)
\( = \frac{{\sin 700\pi t}}{{700\pi t}} + \frac{{\sin 500\pi t}}{{500\pi t}}\)
f1 = 700π/2π = 350 Hz
f2 = 500π/2π = 250 Hz
fm = max (f1, f2) = max (350, 250) = 350 Hz
Sampling frequency,
fs = 2fm = 2 × 350 = 700 Hz
Sampling time period = 1/700 sec