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With James Cooley, created the fast Fourier transform. He invented the term "bit". [57] 1936 Turing, Alan: Made several fundamental contributions to theoretical computer science, including the Turing machine computational model, the conceiving of the stored program concept and the designing of the high-speed ACE design.
Steven Glenn Johnson (born 1973) [2] is an American applied mathematician and physicist known for being a co-creator of the FFTW [3] [4] [5] library for software-based fast Fourier transforms and for his work on photonic crystals. He is professor of Applied Mathematics and Physics at MIT where he leads a group on Nanostructures and Computation. [6]
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency.
An example FFT algorithm structure, using a decomposition into half-size FFTs A discrete Fourier analysis of a sum of cosine waves at 10, 20, 30, 40, and 50 Hz. A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT).
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 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).
The discrete version of the Fourier transform (see below) can be evaluated quickly on computers using fast Fourier transform (FFT) algorithms. [8] In forensics, laboratory infrared spectrophotometers use Fourier transform analysis for measuring the wavelengths of light at which a material will absorb in the infrared spectrum.
Jean-Baptiste Joseph Fourier (/ ˈ f ʊr i eɪ,-i ər /; [1] French: [ʒɑ̃ batist ʒozɛf fuʁje]; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations.