Fourier transform fringe-pattern analysis is a wide-spread technique with many applications to optical metrology. Introducing a spatial carrier into a holographic moiré pattern is also a well-known technique to obtain observable moiré fringes. Preprocessing of the holographic moiré pattern includes optical or digital Fourier filtering to remove the carrier. The pattern is then processed by employing time-consuming and less accurate fringe-counting algorithms. This work presents a new application of the Fourier transform method to automated analysis of holographic moiré fringe patterns. The method has the advantage of instantaneous determination of both phase functions in the fringe pattern. Investigations are carried out on the frequency limitation imposed on the spatial carrier. The technique is demonstrated on computer-generated noisy holographic moiré patterns. The technique does not complicate the conventional holographic moiré arrangement.