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The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete Fourier transform (DFT) of an arbitrary composite size = in terms of N 1 smaller DFTs of sizes N 2, recursively, to reduce the computation time to O(N log N) for highly composite N (smooth numbers).
This category is for fast Fourier transform (FFT) algorithms, i.e. algorithms to compute the discrete Fourier transform (DFT) in O(N log N) time (or better, for approximate algorithms), where is the number of discrete points.
The Fastest Fourier Transform in the West (FFTW) is a software library for computing discrete Fourier transforms (DFTs) developed by Matteo Frigo and Steven G. Johnson at the Massachusetts Institute of Technology. [2] [3] [4] FFTW is one of the fastest free software implementations of the fast Fourier transform (FFT).
The development of fast algorithms for DFT can be traced to Carl Friedrich Gauss's unpublished 1805 work on the orbits of asteroids Pallas and Juno.Gauss wanted to interpolate the orbits from sample observations; [6] [7] his method was very similar to the one that would be published in 1965 by James Cooley and John Tukey, who are generally credited for the invention of the modern generic FFT ...
The hexagonal fast Fourier transform (HFFT) uses existing FFT routines to compute the discrete Fourier transform (DFT) of images that have been captured with hexagonal sampling. [1] The hexagonal grid serves as the optimal sampling lattice for isotropically band-limited two-dimensional signals and has a sampling efficiency which is 13.4% ...
A decimation-in-time radix-2 FFT breaks a length-N DFT into two length-N/2 DFTs followed by a combining stage consisting of many butterfly operations. More specifically, a radix-2 decimation-in-time FFT algorithm on n = 2 p inputs with respect to a primitive n -th root of unity ω n k = e − 2 π i k n {\displaystyle \omega _{n}^{k}=e^{-{\frac ...
Rader's algorithm (1968), [1] named for Charles M. Rader of MIT Lincoln Laboratory, is a fast Fourier transform (FFT) algorithm that computes the discrete Fourier transform (DFT) of prime sizes by re-expressing the DFT as a cyclic convolution (the other algorithm for FFTs of prime sizes, Bluestein's algorithm, also works by rewriting the DFT as a convolution).
The run-time bit complexity to multiply two n-digit numbers using the algorithm is ( ) in big O notation. The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007.