The Nyquist sampling interval, for the signal sinc(700t) + sinc(500t) is:

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  1. \(\frac{1}{{350}}sec\)
  2. \(\frac{\pi }{{350}}sec\)
  3. \(\frac{1}{{700}}sec\)
  4. \(\frac{\pi }{{175}}sec\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{1}{{700}}sec\)
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Detailed Solution

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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

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