VLSI computations: from physics to algorithms

Fast fourier transforms: A tutorial review and a state of the art

“…As a measure of efficiency both chip area (A) and time (T) between two successive DFT computations (set-up times are neglected since only throughput is of interest) are of importance. Asymptotic lower bounds for the product A-T 2 have been reported for the FFT [116] and lead to ~(2AT2(DFT(N)) = N 2 log2(N), (78) that is, no circuit will achieve a better behavior than (78) for large N. Interestingly, this lower bound is achieved by several algorithms, notably the algorithms based on shuffle-exchange networks and the ones based on square grids [96,114]. The trouble with these optimal schemes is that they outperform more traditional ones, like the cascade connection with variable delay [98] (which is asymptotically sub-optimal), only for extremely large Ns and are therefore not relevant in practice [96].…”