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The fractional Fourier transform and applicationsThis paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
Document ID
19920037310
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Bailey, David H.
(NASA Ames Research Center Moffett Field, CA, United States)
Swarztrauber, Paul N.
(NASA Ames Research Center Moffett Field, CA; NCAR, Boulder, CO, United States)
Date Acquired
August 15, 2013
Publication Date
September 1, 1991
Publication Information
Publication: SIAM Review
Volume: 33
ISSN: 0036-1445
Subject Category
Numerical Analysis
Funding Number(s)
CONTRACT_GRANT: NCC2-387
Distribution Limits
Public
Copyright
Other
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