What is the inverse Fourier transform of \(X\left( \omega \right) = {e^{ - \frac{{\left| \omega \right|}}{2}}}\)
1
\(\frac{2}{{1 + 4{t^2}}}\)
2
\(\frac{2}{{\pi \left( {1 + {t^2}} \right)}}\)
3
\(\frac{2}{{1 + {t^2}}}\)
4
\(\frac{2}{{\pi \left( {1 + 4{t^2}} \right)}}\)