GATE EE 2023 Set 1 — Question 18
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Signals & Systems → Fourier Analysis & Sampling → CTFT & DTFT
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Question
The Fourier transform of the signal is given byWhich one of the following statements is true?
Correct answer
(A) x(t) tends to be an impulse as W₀ → ∞.
Solution
1.Find the inverse Fourier transform :
2.Evaluate statement (A):
As , for all . The inverse Fourier transform of a constant 1 is the Dirac delta function . Thus, , which is an impulse. Statement (A) is true.3.Evaluate statement (B):
As increases, increases. Statement (B) is false.4.Evaluate statements (C) and (D):
At :This value depends on and is not a constant . Statements (C) and (D) are false.Therefore, the correct option is (A).
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