GATE EC 2025 Set 1 — Question 18
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Signals & Systems → Continuous-Time Signals → Fourier Transform & Properties
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Question
Consider a continuous-time, real-valued signal whose Fourier transform exists.Which one of the following statements is always TRUE?
Correct answer
(A) F(ω) ≤ ∫_(-∞)^(∞) f(t) dt
Solution
The Fourier transform is defined as . Taking the absolute value on both sides: . By the integral triangle inequality, . Applying this: . Since for real and , we have . This inequality holds for all . Thus, statement (A) is always true.
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