The Fourier transform $X(\omega)$ of $x(t)=e^{-t^{2}}$ is
Note: $\int_{-\infty}^{\infty} e^{-y^{2}} d y=\sqrt{\pi}$
- $\sqrt{\pi} e^{\frac{\omega^{2}}{2}}$
- $\frac{e^{-\frac{\omega^{2}}{4}}}{2 \sqrt{\pi}}$
- $\sqrt{\pi} e^{-\frac{\omega^{2}}{4}}$
- $\sqrt{\pi} e^{-\frac{\omega^{2}}{2}}$