The Fourier transform of the position wave for a particle yields the space frequency wave of the particle in the same way that the Fourier transform of a picture gives you the spatial frequency of that picture.

We can then relate the spatial frequency of a photon to its momentum by the formula p = h * f / c, where h and c are the Planck constant and the speed of light in a vacuum, respectively. From this we see that the momentum of a photon is a function of frequency, which, from the properties of the Fourier transform, we know to be the conjugate pair of position.