Let $g(t) = e^{-\pi t^{2}},$ and $h(t)$ is a filter matched to $g(t).$ If $g(t)$ is applied as input to $h(t),$ then the Fourier transformation of the output is
1. $e^{-\pi f^{2}}$
2. $e^{-\pi f^{2}/ 2}$
3. $e^{-\pi \mid f \mid }$
4. $e^{-2\pi f^{2}}$