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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 ...
Algorytm Cooleya-Tukeya – algorytm szybkiej transformacji Fouriera (FFT). Wyraża dyskretną transformację Fouriera (DFT) o dowolnej złożonej wielkości w członach mniejszych DFT wielkości i rekurencyjnie, w celu ograniczenia czasu obliczeń do szczególnie w przypadku będącego liczbą wysoce złożoną (liczbą gładką).
The Cooley-Tukey algorithm makes the observation that if our number of samples is a power of 2, then we end up with summations of length 1. In other words, we subdivide the summations all the way down to transforms of length 1.
17 lut 2024 · The discovery of the Fast Fourier transformation (FFT) is attributed to Cooley and Tukey, who published an algorithm in 1965. But in fact the FFT has been discovered repeatedly before, but the importance of it was not understood before the inventions of modern computers.
It is described first in Cooley and Tukey’s classic paper in 1965, but the idea actually can be traced back to Gauss’s unpublished work in 1805. It is a divide and conquer algorithm that recursively breaks the DFT into smaller DFTs to bring down the computation.
The publication by Cooley and Tukey in 1965 of an efficient algorithm for the calculation of the DFT was a major turning point in the development of digital signal processing. During the five or so years that followed, various extensions and modifications were made to the original algorithm.
In this section, we’ll see one of the earliest methods, (re-)discovered in 1965 by Cooley and Tukey , which can accelerate DFT calculations when \(N\) is an integral power of 2: \(N = 2^K\). The Cooley-Tukey method for DFT calculation was known to Gauss all the way back in the early 19th century.
