Category: FFT algorithms

Sliding DFT
In applied mathematics, the sliding discrete Fourier transform is a recursive algorithm to computesuccessive STFTs of input data frames that are a single sampleapart (hopsize − 1).
Prime-factor FFT algorithm
The prime-factor algorithm (PFA), also called the Good–Thomas algorithm (1958/1963), is a fast Fourier transform (FFT) algorithm that re-expresses the discrete Fourier transform (DFT) of a size N = N1
Twiddle factor
A twiddle factor, in fast Fourier transform (FFT) algorithms, is any of the trigonometric constant coefficients that are multiplied by the data in the course of the algorithm. This term was apparently
Bit-reversal permutation
In applied mathematics, a bit-reversal permutation is a permutation of a sequence of items, where is a power of two. It is defined by indexing the elements of the sequence by the numbers from to , rep
Split-radix FFT algorithm
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 (1968) and subse
Butterfly diagram
In the context of fast Fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete Fourier transforms (DFTs) into a larger DFT, or vice vers
Cooley–Tukey FFT algorithm
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 com
Bruun's FFT algorithm
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 arbitra
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 o
Rader's FFT algorithm
Rader's algorithm (1968), 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-expr
Cyclotomic fast Fourier transform
The cyclotomic fast Fourier transform is a type of fast Fourier transform algorithm over finite fields. This algorithm first decomposes a DFT into several circular convolutions, and then derives the D
Vector-radix FFT algorithm
The vector-radix FFT algorithm, is a multidimensional fast Fourier transform (FFT) algorithm, which is a generalization of the ordinary Cooley–Tukey FFT algorithm that divides the transform dimensions
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
Chirp Z-transform
The chirp Z-transform (CZT) is a generalization of the discrete Fourier transform (DFT). While the DFT samples the Z plane at uniformly-spaced points along the unit circle, the chirp Z-transform sampl
Goertzel algorithm
The Goertzel algorithm is a technique in digital signal processing (DSP) for efficient evaluation of the individual terms of the discrete Fourier transform (DFT). It is useful in certain practical app
Irrational base discrete weighted transform
In mathematics, the irrational base discrete weighted transform (IBDWT) is a variant of the fast Fourier transform using an irrational base; it was developed by Richard Crandall (Reed College), (Dartm
Fast Fourier transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (oft