Space-time trade-offs on the FFT algorithm

The performance of the fast Fourier transfmm algorithm is examined under limitations on computational space and time. It is shown that if the algorithm with n inputs, n as a power of two, is implemented with S temporary locations where S=o(n/ \log n) , then the computation time T grows faster than n \log n . Furthermore, T can grow as fast as n^{2} if S=S_{min} + O(1) where S_{min}=l+\log_{2}n , the minimum necessary. These results are obtained by deriving tight bounds on T versus S and n .