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GATE 2025 BM – Question 36

Signals and Systems · Signals and Sampling · 2 marks · Multiple choice

For $x(t)=20\sin(100\pi t)+36\sin(150\pi t)-2\sin(300\pi t)$ with t in seconds, which sampling frequency permits accurate reconstruction?

  1. 500 Hz
  2. 150 Hz
  3. 200 Hz
  4. 250 Hz

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Correct answer: (A) 500 Hz

Explanation

The component frequencies are fifty,seventy-five and one hundred fifty hertz. Reconstruction requires sampling above twice the highest frequency, or above three hundred hertz. Only five hundred hertz among the options meets this requirement, A.

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