GATE EC 2016 Set 3 — Question 17
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Signals & Systems → Continuous-Time Signals → Fourier Transform & Properties
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Question
If the signal with denoting the convolution operation, then is equal to
Correct answer
(A) \sin(t){\pi t}
Solution
Let . Its Fourier transform is .
Convolution in the time domain corresponds to multiplication in the frequency domain:
.
Taking the inverse Fourier transform, we get .
Convolution in the time domain corresponds to multiplication in the frequency domain:
.
Taking the inverse Fourier transform, we get .
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