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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).
Bruun's algorithm is a fast Fourier transform (FFT) algorithm based on an unusual recursive polynomial-factorization approach, proposed for powers of two by G. Bruun in 1978 and generalized to arbitrary even composite sizes by H. Murakami in 1996.
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).
FFTPACK is a package of Fortran subroutines for the fast Fourier transform.It includes complex, real, sine, cosine, and quarter-wave transforms.It was developed by Paul Swarztrauber of the National Center for Atmospheric Research, and is included in the general-purpose mathematical library SLATEC.
The Bailey's FFT (also known as a 4-step FFT) is a high-performance algorithm for computing the fast Fourier transform (FFT). This variation of the Cooley–Tukey FFT algorithm was originally designed for systems with hierarchical memory common in modern computers (and was the first FFT algorithm in this so called "out of core" class).
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 split-radix FFT is a fast Fourier transform (FFT) algorithm for computing the discrete Fourier transform (DFT), and was first described in an initially little-appreciated paper by R. Yavne (1968) and subsequently rediscovered simultaneously by various authors in 1984.
With an FFT based spectrum analyzer, the frequency resolution is = /, the inverse of the time T over which the waveform is measured and Fourier transformed. With Fourier transform analysis in a digital spectrum analyzer, it is necessary to sample the input signal with a sampling frequency that is at least twice the bandwidth of the signal, due ...