Einhüllende eines Wellenpaktes

<< Graphics`Graphics`

Integrate[
      1/(k^2 + α^2) Sin[
          x k], {k, -∞, ∞}]

Integrate[
      1/(k^2 + α^2) Cos[
          x k], {k, -∞, ∞}]

α = 1;

DisplayTogether[
      Plot[(E^(-x (Sqrt[(α^2)]) Sign[x])) , {x, -5, 
          5}], ImageSize -> 550]

DisplayTogether[
      Plot[α/π/(k^2 + α^2) , {k, -5, 5}], 
      ImageSize -> 550]