# An algorithm for the machine calculation of complex Fourier series

```@article{Cooley1965AnAF,
title={An algorithm for the machine calculation of complex Fourier series},
author={James W. Cooley and John W. Tukey},
journal={Mathematics of Computation},
year={1965},
volume={19},
pages={297-301}
}```
• Published 1 May 1965
• Computer Science
• Mathematics of Computation
An efficient method for the calculation of the interactions of a 2' factorial ex- periment was introduced by Yates and is widely known by his name. The generaliza- tion to 3' was given by Box et al. (1). Good (2) generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series. In their full generality, Good's methods are applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored…
11,510 Citations

### Note on the calculation of Fourier series

A small-computer program has been written in this laboratory which uses the Danielson-Lanezos method with one minor modification, described below, and yields the same results as the binary form of the Cooley-Tukey algorithm with a comparable number of arithmetical operations.

### Gauss and the history of the fast Fourier transform

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• 1984
The algorithm developed by Cooley and Tukey clearly had its roots in, though perhaps not a direct influence from, the early twentieth century, and remains the most Widely used method of computing Fourier transforms.

### Algorithms: Algorithm 339: an algol procedure for the fast Fourier transform with arbitrary factors

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### An Adaptation of the Fast Fourier Transform for Parallel Processing

A modified version of the Fast Fourier Transform is developed and described and it is suggested that this form is of general use in the development and classification of various modifications and extensions of the algorithm.

### Algorithms: Algorithm 340: roots of polynomials by a root-squaring and resultant routine

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### Algorithms: Algorithm 341: solution of linear programs in 0-1 variables by implicit enumeration

• Mathematics
CACM
• 1968
The following procedures are based on the Cooley-Tukey algor i thm [1] for comput ing the finite Fourier t r ans fo rm of a complex da ta vector; the dimension of the da t a vector is assumed here to

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This work describes an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension and proposes a careful study of the method that leads to a precise estimation of the complexity in terms of the number of points and chosen accuracy.

### Practical Algorithm For Computing The 2-D Arithmetic Fourier Transform

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This new 2-D AFT algorithm is based on both the number-theoretic method of Mobius inversion of double series and the complex conjugate property of Fourier coefficients and is readily suitable for VLSI implementation as a parallel architecture.

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A one-dimensional Discrete Fourier Transform (DFT) is defined to be a linear transform which satisfies the convolution property: a convolution can be performed on two vectors by performing a DFT on

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• Computer Science
• 1954
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