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

  1. $\sqrt{\pi} e^{\frac{\omega^{2}}{2}}$
  2. $\frac{e^{-\frac{\omega^{2}}{4}}}{2 \sqrt{\pi}}$
  3. $\sqrt{\pi} e^{-\frac{\omega^{2}}{4}}$
  4. $\sqrt{\pi} e^{-\frac{\omega^{2}}{2}}$
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