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. FFTW is one of the fastest free software implementations of the fast Fourier transform (FFT). It implements the FFT algorithm for real and complex-valued arrays of arbitrary size and dimension. FFTW expeditiously transforms data by supporting a variety of algorithms and choosing the one (a particular decomposition of the transform into smaller transforms) it estimates or measures to be preferable in the particular circumstances. It works best on arrays of sizes with small prime factors, with powers of two being optimal and large primes being worst case (but still O(n log n)). To decompose transforms of composite sizes into smaller transforms, it chooses among several variants of the Cooley–Tukey FFT algorithm (corresponding to different factorizations and/or different memory-access patterns), while for prime sizes it uses either Rader's or Bluestein's FFT algorithm. Once the transform has been broken up into subtransforms of sufficiently small sizes, FFTW uses hard-coded unrolled FFTs for these small sizes that were produced (at compile time, not at run time) by code generation; these routines use a variety of algorithms including Cooley–Tukey variants, Rader's algorithm, and prime-factor FFT algorithms. More information...

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