GATE EC 2022 Set 1 — Question 15
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Signals & Systems → Continuous-Time Signals → Fourier Transform & Properties
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Question
The Fourier transform of the signal is _________.
Correct answer
(A) (π)/(2j) ω e^(- ω)
Solution
We know the Fourier transform pair: .
By the duality property: .
Using the differentiation in time property: .
Let , then .
.
Taking the Fourier transform of both sides:
.
By the duality property: .
Using the differentiation in time property: .
Let , then .
.
Taking the Fourier transform of both sides:
.
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