GATE Electrical 2023 | Question: 8

Question

The Fourier transform $X(\omega)$ of the signal $x(t)$ is given by

$$\begin{aligned}
X(\omega) & =1, \text { for }|\omega|<W_o \\
& =0, \text { for }|\omega|>W_0
\end{aligned}$$

Which one of the following statements is true?

• A. $x(t)$ tends to be an impulse as $W_0 \rightarrow \infty$.
• B. $x(0)$ decreases as $W_0$ increases.
• C. At $t=\frac{\pi}{2 W_0}, x(t)=-\frac{1}{\pi}$
• D. At $t=\frac{\pi}{2 W_0}, x(t)=\frac{1}{\pi}$