The problem of the behavior of a pulse when propagating through a dispersive medium has been treated in terms of Fourier transforms. For a linearly dispersive medium the evaluation of the integrals is trivial, but when the dispersion relation contains a significant quadratic term the integrals can be evaluated using the properties of Fresnel integrals. The advantage of this treatment is that it shows that there is a very strong analogy between the pulse shape and the diffraction pattern produced when light passes through a small hole in an opaque screen.