GATE 2016 EC – Question 20
A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of 23 Hz. The fundamental frequency (in Hz) of the output is ________
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Correct answer: 12 to 14
Explanation
Multiplying by an impulse train of frequency 46 Hz gives components at $\pm 33 + 46k$ Hz, which are $33, 13, 59, 79, \ldots$ and the mirror images $-33, -13, \ldots$. The low-pass filter with a 23 Hz cutoff passes only the 13 Hz component, since $|46 - 33| = 13 < 23$, and blocks 33 Hz. The output is a 13 Hz sinusoid.