A unified treatment of Cooley-Tukey algorithms for the evaluation of the multidimensional DFT

Mersereau, R.M.; Speake, T.

doi:10.1109/tassp.1981.1163687

Cited by 56 publications

(19 citation statements)

References 11 publications

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“…A computationally more efficient way of performing the 2-D FFT is a direct approach to the multi-dimensional problem: the vector-radix (VR) algorithm [91,92,85].…”

Section: Vector-radix Algorithmsmentioning

confidence: 99%

Fast fourier transforms: A tutorial review and a state of the art

Duhamel¹,

1990

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Rrsum4. La publication de l'algorithme de Cooley-Tukey pour la transformation de Fourier rapide a ouvert une nouvelle ~re dans le traitement num6rique des signaux, en r4duisant l'ordre de complexit6 de probl~mes cruciaux, comme la transformation de Fourier ou la convolution, de N 2 ~ N log2 N (oh N est la taille du probl~me). Le drvelopment des algorithmes principaux (Cooley-Tukey, split-radix FFT, algorithmes des facteurs premiers, et transform6e rapide de Winograd) est drcrit. Ensuite, l'&at de l'art est donn4, et on parle des probl~mes ouverts et des implantations.

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“…A computationally more efficient way of performing the 2-D FFT is a direct approach to the multi-dimensional problem: the vector-radix (VR) algorithm [91,92,85].…”

Section: Vector-radix Algorithmsmentioning

confidence: 99%

Fast fourier transforms: A tutorial review and a state of the art

Duhamel¹,

1990

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“…The algorithm of Cooley and Tukey is extended in [3] to the computation of (3) and (4). Such an extension assumes that N = PQ, with P and Q integer matrixes.…”

Section: Xeitmentioning

confidence: 99%

“…Expression (6) shows that the computation of the DFT by means of the algorithm of [3] corresponds to the computation of a sequence of DFT (of type (3)) followed by the corresponding twiddle-factors multiplication. It is important to note that the output-data of the i-th DFT, denoted as Xi(pl,pz,.…”

Section: Xeitmentioning

confidence: 99%

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A general scrambling rule for multidimensional Cooley-Tukey FFT algorithms

Bernardini¹,

Cortelazzo²,

Mian³

1993

IEEE International Conference on Acoustics Speech and Signal Processing

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This work determines the scrambling rule of the multidimensional Cooley-Tukey F F T for signals defined on general lattices. Previous work has only addressed the scrambling relative to ortogonal lattices. An area where multidimensional lattices of general type are used is video signal processing. These results can be profitably applied to the spectral analysis and the fast c e volution of video sequences.

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“…An elegant solution to the above problem has been proposed in [3]. The present work deals with a different, metric approach to the problem of unification of schemes of the DFT-2 decomposition.…”

Section: Introductionmentioning

confidence: 99%

A metric unified treatment of two-dimensional FFT

Chernov

1996

Proceedings of 13th International Conference on Pattern Recognition

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A unification of fast algorithms for the discrete Fourier transform is discussed. A relationship is established with the coverings of sets of input data indices and their metric properties with respect to the families of non-Archimedean metrics. A n explicit analogy is given between the basic relations f o r the FFT-2 decomposition and the Stokes theorem on manifolds. Fast Fourier Transforms with reduced computational complexity are synrhesized.

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A unified treatment of Cooley-Tukey algorithms for the evaluation of the multidimensional DFT

Cited by 56 publications

References 11 publications

Fast fourier transforms: A tutorial review and a state of the art

Fast fourier transforms: A tutorial review and a state of the art

A general scrambling rule for multidimensional Cooley-Tukey FFT algorithms

A metric unified treatment of two-dimensional FFT

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