The Fourier transform $$X(\omega)$$ of the signal $$x(t)$$ is given by $$X(\omega ) = 1$$, for $$|\omega | $$ = 0$$, for $$|\omega | > {W_0}$$ Which one of the following statements is true?

$$x(t)$$ tends to be an impulse as $${W_0} \to \infty $$.

$$x(0)$$ decreases as $${W_0}$$ increases.

At $$t = {\pi \over {2{W_0}}},x(t) = - {1 \over \pi }$$

At $$t = {\pi \over {2{W_0}}},x(t) = {1 \over \pi }$$

GATE 2023 Electrical Engineering PYQ — Signals and Systems

GATE 20232023PYQMCQanswer keyexplanationeasy

Signals and Systems · Fourier (EE)

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Recurring concept

Fourier (EE) has appeared in GATE Electrical Engineering 28 times across 16 years (2021, 2022, 2023, 2024, 2025, ...).