GATE EC 2024 Set 1 — Question 44
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Signals & Systems → Continuous-Time Signals → Fourier Transform & Properties
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Question
Consider two continuous time signals and as shown below
If denotes the Fourier transform of , then the Fourier transform of is _______.
Correct answer
(B) -4X(4f)e^(-j4π f)
Solution
Let be a standard triangular pulse defined from to with peak height at . Its Fourier transform is .
By the scaling property, .
By scaling and shifting properties:
Rearranging for :
Substitute this into the expression for :
Thus, the correct option is (B).
1.Analyze :
is a triangle from to with height . Thus, .By the scaling property, .
2.Analyze :
is a triangle from to with height . It is a shifted and scaled version of :By scaling and shifting properties:
Rearranging for :
3.Relate to :
We need . From , replace with :Substitute this into the expression for :
Thus, the correct option is (B).
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