GATE EC 2014 Set 2 — Question 62
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Communications → Analog Communications → AM & FM Spectra
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Question
In the figure, is the Fourier transform of the message signal where Hz and Hz. Given and , where . The cutoff frequencies of both the filters are .
The bandwidth of the signal at the output of the modulator (in Hz) is _____.
Correct answer
59.9 to 60.1
Solution
1.The message signal has a spectrum that is non-zero in the range .
2.Multiplying by shifts the spectrum to . The positive frequency components are in the range .
3.The High Pass Filter (HPF) has a cutoff frequency of . It passes frequencies greater than , which corresponds to the Upper Side Band (USB): .
4.This signal is then multiplied by . This shifts the USB spectrum by .
5.The difference frequency components are .
6.The Low Pass Filter (LPF) has a cutoff frequency of . Since Hz and , the baseband signal Hz passes through.
7.The bandwidth of the resulting signal is Hz.
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