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An algorithm for computing the mixed radix fast Fourier transform
Abstract
This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey. As in their algorithm, the dimensionnof the transform is factored (if possible), andn/pelementary transforms of dimensionpare computed for each factorpofn. An improved method of computing a transform step corresponding to an odd factor ofnis given; with this method, the number of complex multiplications for an elementary transform of dimensionpis reduced from(p-1)^{2}to(p-1)^{2}/4for oddp. The fast Fourier transform, when computed in place, requires a final permutation step to arrange the results in normal order. This algorithm includes an efficient method for permuting the results in place. The algorithm is described mathematically and illustrated by a FORTRAN subroutine.
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Citations
Cites
An algorithm for the machine calculation of complex Fourier series
Cooley, J. W., & Tukey, J. W. (1965) · Mathematics of Computation · doi:10.1090/s0025-5718-1965-0178586-1 · Cited by 13,154
Cited by
The Design and Implementation of FFTW3
Frigo, M., & Johnson, S. G. (2005) · Proceedings of the IEEE · doi:10.1109/jproc.2004.840301 · Cited by 5,086
Frigo, M., Leiserson, C. E., Prokop, H., & Ramachandran, S. (2003) · 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039) · doi:10.1109/sffcs.1999.814600 · Cited by 803
Maronga, B., Gryschka, M., Heinze, R., Hoffmann, F., Kanani-Sühring, F., Keck, M., Ketelsen, K., Letzel, M. O., Sühring, M., & Raasch, S. (2015) · Geoscientific Model Development · doi:10.5194/gmd-8-2515-2015 · Cited by 553
Three-dimensional reconstruction of single particles embedded in ice
Penczek, P., Radermacher, M., & Frank, J. (1992) · Ultramicroscopy · doi:10.1016/0304-3991(92)90233-a · Cited by 458
Netravali, A. N., & Limb, J. O. (1980) · Proceedings of the IEEE · doi:10.1109/proc.1980.11647 · Cited by 451
Metadata
- Authors
- Singleton, R.
- Venue
- IEEE Transactions on Audio and Electroacoustics
- Published
- 1969-06
- Volume
- 17
- Issue
- 2
- Pages
- 93-103
- ISSN
- 0018-9278 (ISSN-L)
- OpenAlex
- W2073086065
- Cited by
- 539
- References
- 1
- FWCI
- 6.85
- Type
- journal article
- Language
- en
- Open access
- closed
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- Singleton, R. (1969). An algorithm for computing the mixed radix fast Fourier transform. IEEE Transactions on Audio and Electroacoustics. https://doi.org/10.1109/tau.1969.1162042
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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