The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
An Adaptation of the Fast Fourier Transform for Parallel Processing
Open accessAbstract
A modified version of the Fast Fourier Transform is developed and described. This version is well adapted for use in a special-purpose computer designed for the purpose. It is shown that only three operators are needed. One operator replaces successive pairs of data points by their sums and differences. The second operator performs a fixed permutation which is an ideal shuffle of the data. The third operator permits the multiplication of a selected subset of the data by a common complex multiplier. If, as seems reasonable, the slowest operation is the complex multiplications required, then, for reasonably sized date sets—e.g. 512 complex numbers—parallelization by the method developed should allow an increase of speed over the serial use of the Fast Fourier Transform by about two orders of magnitude. It is suggested that a machine to realize the speed improvement indicated is quite feasible. The analysis is based on the use of the Kronecker product of matrices. It is suggested that this form is of general use in the development and classification of various modifications and extensions of the algorithm.
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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
Fast 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
What is the fast Fourier transform?
Cochran, W., Cooley, J., Favin, D., Helms, H., Kaenel, R., Lang, W., Maling, G., Nelson, D., Rader, C., & Welch, P. (1967) · IEEE Transactions on Audio and Electroacoustics · doi:10.1109/tau.1967.1161899 · Cited by 490
High-speed convolution and correlation
Stockham, T. G. (1966) · Proceedings of the April 26-28, 1966, Spring joint computer conference on XX - AFIPS '66 (Spring) · doi:10.1145/1464182.1464209 · Cited by 319
Historical 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
Singleton, R. C. (1967) · IEEE Transactions on Audio and Electroacoustics · doi:10.1109/tau.1967.1161906 · Cited by 119
Fast Fourier transform method of computing difference equations and simulating filters
Helms, H. D. (1967) · IEEE Transactions on Audio and Electroacoustics · doi:10.1109/tau.1967.1161905 · Cited by 109
Cited by
Parallel Processing with the Perfect Shuffle
Stone, H. S. (1971) · IEEE Transactions on Computers · doi:10.1109/t-c.1971.223205 · Cited by 1,245
Metadata
- Authors
- Pease, M. C.
- Venue
- Journal of the ACM
- Published
- 1968-04
- Volume
- 15
- Issue
- 2
- Pages
- 252-264
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W1979502974
- Cited by
- 381
- References
- 7
- FWCI
- 15.87
- Type
- journal article
- Language
- en
- Open access
- bronze
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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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