GATE 2017 EC (EC2) – Question 59
The signal $x(t)=\sin(14000\pi t)$, with t in seconds, is sampled at 9000 samples/s. The sampled signal passes through an ideal low-pass filter with $H(f)=1$ for $|f|\le12$ kHz and zero otherwise. The number of output sinusoids and their frequencies (in kHz) are
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Correct answer: (B) Number = 3, frequencies = 2, 7, 11
Explanation
The input sinusoid has frequency 7 kHz, so its spectral lines are at ±7 kHz. Ideal sampling repeats these lines at integer multiples of 9 kHz.
Inside the filter passband, the positive-frequency lines occur at 7, $9-7=2$ and $18-7=11$ kHz, along with their negative-frequency partners. The next images lie outside ±12 kHz.
Each positive/negative pair forms one real sinusoid. Hence there are **three sinusoids at 2, 7 and 11 kHz, B**.