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GATE ECE 2002 | Question: 2.20

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A signal $x(t)=100 \cos \left(24 \pi \times 10^{3}\right) t$ is ideally sampled with a sampling period of $50 \; \mu \mathrm{sec}$ and then passed through an ideal lowpass filter with cut-off frequency of $15 \; \mathrm{kHz}$. Which of the following frequencies is/are present at the filter output?

  1. $12 \; \mathrm{kHz}$ only
  2. $8 \; \mathrm{kHz}$ only
  3. $12 \; \mathrm{kHz}$ and $9 \; \mathrm{kHz}$
  4. $12 \; \mathrm{kHz}$ and $8 \; \mathrm{KHz}$

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