GATE 2014 EC (EC3) – Question 29
$y(t)=m(t)\cos(40000\pi t)$, where m(t) contains only frequencies below 5 kHz. Find the minimum sampling rate for y(t) that permits recovery of m(t) (kHz).
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Correct answer: 9.5 to 10.5
Explanation
The carrier is20kHz and the message is bandlimited below5kHz. Sampling at10kHz makes cos(40000πn/10000)=cos(4πn)=1, so the sampled modulated signal equals the message samples. A rate10kHzis the message Nyquist limit and permits recovery under the stated strict bandlimit. Thus **10kHz** uses bandpass sampling; ordinary low-pass sampling of the full RF waveform would require50kHz.