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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 direct calculation of the constant-Q transform (either using naive discrete Fourier transform or slightly faster Goertzel algorithm) is slow when compared against the fast Fourier transform. However, the fast Fourier transform can itself be employed, in conjunction with the use of a kernel , to perform the equivalent calculation but much ...
The multitaper method overcomes some of the limitations of non-parametric Fourier analysis. When applying the Fourier transform to extract spectral information from a signal, we assume that each Fourier coefficient is a reliable representation of the amplitude and relative phase of the corresponding component frequency. This assumption, however ...
The field of digital signal processing relies heavily on operations in the frequency domain (i.e. on the Fourier transform). For example, several lossy image and sound compression methods employ the discrete Fourier transform: the signal is cut into short segments, each is transformed, and then the Fourier coefficients of high frequencies ...
Signal-flow graph connecting the inputs x (left) to the outputs y that depend on them (right) for a "butterfly" step of a radix-2 Cooley–Tukey FFT. This diagram resembles a butterfly (as in the morpho butterfly shown for comparison), hence the name, although in some countries it is also called the hourglass diagram.
Similar to the DFT (discrete Fourier transformation) a frequency domain split into N discrete partitions is obtained. An inverse transformation of these N spectral partitions then leads to N values y ( k ) for the time window, which consists of N sample values.
In structural biology, as well as in virtually all sciences that produce three-dimensional data, the Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3-dimensional volumes over corresponding shells in Fourier space (i.e., as a function of spatial frequency [1]).
In bioinformatics, MAFFT (multiple alignment using fast Fourier transform) is a program used to create multiple sequence alignments of amino acid or nucleotide sequences. Published in 2002, the first version used an algorithm based on progressive alignment , in which the sequences were clustered with the help of the fast Fourier transform . [ 2 ]