The sampling frequency of the signal g(t) = sinc2 (200 t) is

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UPSC IES Electrical 2022 Prelims Official Paper
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  1. 100 Hz
  2. 200 Hz
  3. 400 Hz
  4. 800 Hz

Answer (Detailed Solution Below)

Option 3 : 400 Hz
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Concept: 

Nyquist Sampling interval is defined as the maximum time that:

1) is between regularly spaced samples that will permit the signal waveform to be completely determined.

2) and is equal to reciprocal to twice of the highest frequency in the sampling signal.

i.e., if signal frequency is fm then :

Nyquist rate fs ≥ 2fm

And Nyquist interval:

\({T_s} \le \frac{1}{{2{f_m}}}\)

sinc function: It is the Fourier transform of rectangular function with no scaling.
\(\sin c\left( x \right) = \frac{{\sin \left( x \right)}}{x}\)

\(\sin c\left( x \right) = \left\{ {\begin{array}{*{20}{c}} 1&{x = 0}\\ {\frac{{\sin x}}{x}}&{otherwise} \end{array}} \right.\)

Analysis:

If two or more than two signals are added with signal frequency  then sampling frequency will be:

\({f_s} = 2 \left( {{f_{{m_1}}}+\;{f_{{m_2}}}+\;{f_m}}+.... \right)\)

And \({T_s} = \frac{1}{{{F_s}}}\)

Calculation:

ωm = 2 × (200 + 200) π = 800 π rad/sec

fm = ωm/2π = 400 Hz

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