GATE ECE 2022 | Question: 5

Question

The Fourier transform $X(j \omega)$ of the signal

$$x(t) = \frac{t}{(1+t^{2})^{2}}$$

is ______________.

• A. $\frac{\pi}{2j} \omega e^{– |\omega|}$
• B. $\frac{\pi}{2} \omega e^{– |\omega|}$
• C. $\frac{\pi}{2j}e^{– |\omega|}$
• D. $\frac{\pi}{2}e^{– |\omega|}$