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The fast Fourier transform for experimentalists
Computing in Science & Engineering, 2005In part one of this series, we discussed several basic properties of the fast Fourier transform (FFT). In addition to fundamental elements, we treated zero padding, aliasing, the relationship to a Fourier series, and ended with an introduction to windowing.
Denis Donnelly, Bert W. Rust
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The hexagonal fast fourier transform
2016 IEEE International Conference on Image Processing (ICIP), 2016The discrete Fourier transform is an important tool for processing digital images. Efficient algorithms for computing the Fourier transform are known as fast Fourier transforms (FFTs). One of the most common of these is the Cooley-Tukey radix-2 decimation algorithm that efficiently transforms one-dimensional data into its frequency domain ...
James B. Birdsong, Nicholas I. Rummelt
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A Generalization of the Fast Fourier Transform
IEEE Transactions on Computers, 1970A procedure for factoring of the N×N matrix representing the discrete Fourier transform is presented which does not produce shuffled data. Exactly one factor is produced for each factor of N, resulting in a fast Fourier transform valid for any N. The factoring algorithm enables the fast Fourier transform to be implemented in general with four nested ...
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Integer fast Fourier transform
IEEE Transactions on Signal Processing, 2002A concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has the properties that it is an integer-to-integer mapping, is power adaptable and is reversible.
Soontorn Oraintara +2 more
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Accuracy of the Discrete Fourier Transform and the Fast Fourier Transform
SIAM Journal on Scientific Computing, 1996Accuracy of the discrete Fourier transform (DFT) and the fast Fourier transform (FFT) depends on the accuracy of the twiddle factors entirely. For accurate twiddle factor tables, this paper recommends to compute the sine/cosine functions with high precision arithmetic along the algorithms in terms of faster converging approximations, such as rational ...
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A PARALLEL FAST FOURIER TRANSFORM
International Journal of Modern Physics C, 1999In this paper we discuss the general problem of implementing the multidimensional Fast Fourier Transform algorithm on parallel computers. We show that, on a machine with P processors and fully parallel node communications, the optimal asymptotic scaling behavior of the total computational time with the number of data points, N, given in d dimensions ...
Morante, Silvia +2 more
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2004
Abstract This chapter demonstrates the use of different data distributions in different phases of a parallel fast Fourier transform (FFT), which is a regular computation with a predictable but challenging data access pattern. Both the block and cyclic distributions are used and also intermediates between them.
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Abstract This chapter demonstrates the use of different data distributions in different phases of a parallel fast Fourier transform (FFT), which is a regular computation with a predictable but challenging data access pattern. Both the block and cyclic distributions are used and also intermediates between them.
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On vectorizing the fast fourier transform
BIT, 1980A variant of the Cooley-Tukey algorithm due to Stockham is derived and vectorized and is shown to be on a par with the Pease algorithm. The Stockham algorithm is then proposed for the entire computation of the two-dimensional fast Fourier transform on a vector computer.
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Fast Fourier Transform for Hexagonal Aggregates
Journal of Mathematical Imaging and Vision, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jaime L. Zapata, Gerhard X. Ritter
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Recursive Fast Fourier Transforms
Proceedings of the December 9-11, 1968, fall joint computer conference, part I on - AFIPS '68 (Fall, part I), 1968The development of the Fast Fourier Transform in complex notation has obscured the savings that can be made through the use of recursive properties of trigometric functions. A disadvantage of the Fast Fourier Transform is that all samples of the function must be stored in memory before processing can start. The computation in the Fast Fourier Transform
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