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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}}$
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