Using Fourier methods to reconstruct the phase measured by a wavefront sensor (WFS) can significantly re- duce the number of computations required, as well as easily enable predictive reconstruction methods based on knowledge of the adaptive optics system, atmospheric turbulence and wind profile. Previous work on Fourier re- construction has focused on the Shack-Hartmann WFS. With increasing interest in the highly sensitive Pyramid WFS we present the development of Fourier reconstruction tools tailored to the Pyramid sensor. We include the development of the Fourier model, it’s use for formulating error budgets and a laboratory demonstration of Fourier reconstruction with a Pyramid WFS.