GATE EE 2024 Set 1 — Question 33
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Signals & Systems → Fourier Analysis & Sampling → Fourier Transform Properties
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Question
Let be the Fourier transform of the signal . The value of the derivative of at is _______ (rounded off to 1 decimal place).
Correct answer
0 to 0
Solution
The Fourier transform is defined as:Differentiating with respect to :At :Given . Note that is an even function because .
The integrand is an odd function because .
The integral of an odd function over symmetric limits is zero:Therefore, the derivative at is .
The integrand is an odd function because .
The integral of an odd function over symmetric limits is zero:Therefore, the derivative at is .
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