GATE EC 2020 Set 1 — Question 52
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Communications → Analog Communications → DSB-SC & SSB
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Question
For the modulated signal , the message signal and the carrier frequency is MHz. The signal is passed through a demodulator, as shown in the figure below. The output of the demodulator is
Correct answer
(B) cos(920π t)
Solution
Given:
Modulated signal:
Message signal:
Carrier frequency: HzThe input to the multiplier is and . The output of the multiplier is:Using the trigonometric identity :The first term is a high-frequency component centered at approximately MHz. This will be completely filtered out by the Ideal Low Pass Filter (LPF) with a cut-off frequency of Hz.The second term is:Substituting :Using :The frequencies of these components are:
Hz
HzThe Ideal LPF has a cut-off frequency Hz.
Modulated signal:
Message signal:
Carrier frequency: HzThe input to the multiplier is and . The output of the multiplier is:Using the trigonometric identity :The first term is a high-frequency component centered at approximately MHz. This will be completely filtered out by the Ideal Low Pass Filter (LPF) with a cut-off frequency of Hz.The second term is:Substituting :Using :The frequencies of these components are:
Hz
HzThe Ideal LPF has a cut-off frequency Hz.
- Hz is greater than Hz, so it is rejected.
- Hz is less than Hz, so it passes through the filter.
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