The use of the Fourier transform in the computation of binary star orbits has many advantages over traditional (configuration space) analysis. The method can be applied to visual, spectroscopic and astrometric binaries, as well as to visual binaries where only the separation or position angle is known. While this technique requires the use of a digital computer, the algorithms for implementation of the solutions for the various types of binary star motion are quite similar. A description of the implementation of the astrometric binary solution will be presented along with a discussion of the various estimators for the significance of the derived orbital elements obtained in the course of the solution. If time permits, a summary of some Monte Carlo investigations of the effects of observational noise and temporal sampling on the derived orbital elements will be presented.