The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
The Fast Fourier Transform and Its Applications
Abstract
The advent of the fast Fourier transform method has greatly extended our ability to implement Fourier methods on digital computers. A description of the alogorithm and its programming is given here and followed by a theorem relating its operands, the finite sample sequences, to the continuous functions they often are intended to approximate. An analysis of the error due to discrete sampling over finite ranges is given in terms of aliasing. Procedures for computing Fourier integrals, convolutions and lagged products are outlined.
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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
Self-citationFast Fourier Transforms: for fun and profit
Gentleman, W. M., & Sande, G. (1966) · Proceedings of the November 7-10, 1966, fall joint computer conference on XX - AFIPS '66 (Fall) · doi:10.1145/1464291.1464352 · Cited by 542
The Interaction Algorithm and Practical Fourier Analysis
Good, I. J. (1958) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1958.tb00300.x · Cited by 509
What is the fast Fourier transform?
Cochran, W. T., Cooley, J. W., Favin, D. L., Helms, H. D., Kaenel, R. A., Lang, W. W., Maling, G. C., Nelson, D. E., Rader, C. M., & Welch, P. D. (1967) · Proceedings of the IEEE · doi:10.1109/proc.1967.5957 · Cited by 493
Self-citationHistorical notes on the fast Fourier transform
Cooley, J., Lewis, P., & Welch, P. (1967) · IEEE Transactions on Audio and Electroacoustics · doi:10.1109/tau.1967.1161903 · Cited by 201
Self-citationWhat is Fast Fourier Transform?
Gasmi, A. (2022) · HAL (Le Centre pour la Communication Scientifique Directe) · doi:10.13140/rg.2.2.28731.49444 · Cited by 172
Historical notes on the fast Fourier transform
Cooley, J. W., Lewis, P. A. W., & Welch, P. D. (1967) · Proceedings of the IEEE · doi:10.1109/proc.1967.5959 · Cited by 167
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Cited by
Handbook of Computer Vision Algorithms in Image Algebra
Wilson, J. N., & Ritter, G. X. (2000) · CRC Press eBooks · doi:10.1201/9781420042382 · Cited by 434
Tan, C., Zhao, Y., Wei, S., Gu, G., Liu, P., & Wei, Y. (2024) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v38i5.28310 · Cited by 215
“In Figure 2, we present the mean Fast Fourier Transform (FFT) (Cooley et al. 1969) spectrum of images sampled from various sources.”
MethodInfluentialFrePGAN: Robust Deepfake Detection Using Frequency-Level Perturbations
Jeong, Y., Kim, D., Ro, Y., & Choi, J. (2022) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v36i1.19990 · Cited by 137
Kaleidoscope: An Efficient, Learnable Representation For All Structured Linear Maps
Dao, T., Sohoni, N. S., Gu, A., Eichhorn, M., Blonder, A., Leszczynski, M., Rudra, A., & Ré, C. (2020) · arXiv · doi:10.48550/arxiv.2012.14966 · Cited by 21
Pigment pattern morphospace of Danio fishes: evolutionary diversification and mutational effects
McCluskey, B. M., Liang, Y., Lewis, V. M., Patterson, L. B., & Parichy, D. M. (2021) · Biology Open · doi:10.1242/bio.058814 · Cited by 12
Metadata
- Authors
- Cooley, J. W., Lewis, P. A. W., & Welch, P. D.
- Venue
- IEEE Transactions on Education
- Published
- 1969-03
- Volume
- 12
- Issue
- 1
- Pages
- 27-34
- ISSN
- 0018-9359 (ISSN-L)
- 1557-9638
- OpenAlex
- W2135461721
- Cited by
- 573
- References
- 7
- FWCI
- 7.99
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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