Live briefing
Everything about Cooley–Tukey FFT algorithm
Fast Fourier Transform 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 composite size in terms of N1 smaller DFTs of sizes N2, recursively, to reduce the computation time to O(N log N) for highly composite N (smooth numbers). Because of the algorithm's importance, specific variants and implementation styles have become known by their own names, as described below. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Cooley–Tukey FFT algorithmA 5-minute orientation
- Pick up a classic book: Algorithm designThe most-reprinted book on the subject
- Read the landmark paper: On the two-dimensional vector split-radix FFT algorithmCited 13 times
- Go sideways: Butterfly diagramA closely related topic
- Go sideways: Chirp Z-transformA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
đź“š Books worth reading
Algorithm designMichael T. Goodrich, Roberto Tamassia · 2001
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- 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…
- 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…
- 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…
- 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…
- Fast Fourier transform A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence. A Fourier transform…
- 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…
- Hexagonal fast Fourier transform The hexagonal fast Fourier transform (HFFT) is a tool in image and signal processing which uses fast Fourier transform (FFT) routines to compute the discrete…
- 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…