GATE EC 2014 Set 3 — Question 29
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Signals & Systems → Continuous-Time Signals → Sampling Theorem
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Question
A modulated signal is , where the baseband signal has frequency components less than 5 kHz only. The minimum required rate (in kHz) at which should be sampled to recover is _______.
Correct answer
9.5 to 10.5
Solution
The modulated signal is where kHz. The baseband signal is band-limited to kHz. The spectrum of is . To recover , we can use synchronous demodulation followed by a low-pass filter. If we sample directly, we need to ensure that one of the spectral replicas falls at baseband without aliasing. For a bandpass signal, the minimum sampling rate is where . Here kHz, kHz, kHz. . kHz. However, the question asks for the rate to recover . If we sample at kHz, the replicas of the spectrum at kHz will be shifted by multiples of 10 kHz. Specifically, the replica at kHz shifted by kHz lands at Hz, and the replica at kHz shifted by kHz also lands at Hz. Thus, the baseband signal is reconstructed at baseband. Therefore, the minimum sampling rate is kHz.
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