Time-Space Tradeoffs on Back-to-Back FFT Algorithms

This paper examines the performance of back-to-back applications of a fast Fourier transform algorithm with respect to computational time and space. Using a well-known pebble game as an analysis technique, a lower bound is derived on the product of time and space, which is of the form T · S = Ω(n2 log2n) for an n-input back-to-back FFT. The implications of this lower bound on applications of a back-to-back FFT circuit, such as polynomial multiplication and permutation graphs, are also discussed.