We present a parallel FFT algorithm for SIMD systems following the "Transpose Algorithm" approach. The method is based on the assignment of the data field onto a one-dimensional ring of systolic cells. The systolic array can be universally mapped onto any parallel system. In particular for systems with next-neighbor connectivity our method has the potential to improve the efficiency of matrix transposition by use of hyper-systolic communication. We have realized a scalable parallel FFT on the APE100/Quadrics massively parallel computer, where our implementation is part of a two-dimensional hydrodynamics code for turbulence studies.