Relationships between the Radon–Wigner and fractional Fourier transforms
Abstract
Two recently described transforms are shown to be related. The Radon–Wigner transform is the squared modulus of the fractional Fourier transform. This new theorem may serve to translate signal and image processing results between different signal representations. Some consequences regarding moments are presented, including a new fractional-Fourier-transform uncertainty relation. Implications for processing are suggested.
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The Wigner distribution is the most widely known quadratic time-frequency distribution satisfying the rotation property.
“The most widely known quadratic distribution satisfying the rotation property is the WD”
From Short-time fourier transform: two fundamental properties and an optimal implementation (2003) · cites this paper as [14]
The rotation property implies that the inherent time-frequency domain characteristics of a signal remain unchanged in all fractional Fourier domains.
“It implies that the inherent time-frequency domain characteristics of a signal remains unchanged in all the fractional Fourier domains.”
From Short-time fourier transform: two fundamental properties and an optimal implementation (2003) · cites this paper as [14]
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The discrete fractional Fourier transform
Candan, C., Kutay, M. A., & Ozaktas, H. M. (2000) · IEEE Transactions on Signal Processing · doi:10.1109/78.839980 · Cited by 683 · see citing works
Short-time fourier transform: two fundamental properties and an optimal implementation
Durak, L., & Arikan, O. (2003) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2003.810293 · Cited by 345 · see citing works
Discrete fractional Fourier-transform based on orthogonal projections
Pei, S.-C., Yeh, M.-H., & Tseng, C.-C. (1999) · IEEE Transactions on Signal Processing · doi:10.1109/78.757221 · Cited by 297 · see citing works
A convolution and product theorem for the fractional Fourier transform
Zayed, A. I. (1998) · IEEE Signal Processing Letters · doi:10.1109/97.664179 · Cited by 239 · see citing works
Improved discrete fractional Fourier transform
Pei, S.-C., & Yeh, M.-H. (1997) · Optics Letters · doi:10.1364/ol.22.001047 · Cited by 188 · see citing works
introduction to the fractional fourier transform and its applications
Ozaktas, H. M., Kutay, M. A., & Mendlovic, D. (1999) · Advances in Imaging and Electron Physics · doi:10.1016/s1076-5670(08)70272-6 · Cited by 164 · see citing works
Ozaktas, H. M., & Aytür, O. (1995) · Signal Processing · doi:10.1016/0165-1684(95)00076-p · Cited by 141 · see citing works
Ozaktas, H. M., Erkaya, N., & Kutay, M. A. (1996) · IEEE Signal Processing Letters · doi:10.1109/97.484211 · Cited by 62 · see citing works
The discrete fractional Fourier transform
Candan, C., Kutay, M. A., & Ozaktas, H. M. (1999) · 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258) · doi:10.1109/icassp.1999.756324 · Cited by 52 · see citing works
Nonseparable two-dimensional fractional Fourier transform
Sahin, A., Kutay, M. A., & Ozaktas, H. M. (1998) · Applied Optics · doi:10.1364/ao.37.005444 · Cited by 41 · see citing works
- Authors
- Lohmann, A. W., & Soffer, B. H.
- Affiliations
- Friedrich-Alexander-Universität Erlangen-Nürnberg (DE)
- HRL Laboratories (United States) (US)
- ORCID
- Lohmann, Adolf W.
- Venue
- Journal of the Optical Society of America A
- Publisher
- Optica Publishing Group
- Published
- 1994-06-01
- Volume
- 11
- Issue
- 6
- Pages
- 1798
- ISSN
- 1084-7529 (ISSN-L)
- 1520-8532
- OpenAlex
- W2120230078
- Cited by
- 223
- References
- 0
- Citations by year
- 2025: 3 · 2024: 6 · 2022: 1 · 2021: 2 · 2020: 1 · 2019: 1 · 2017: 3 · 2016: 10 · 2015: 6 · 2014: 3 · 2013: 7 · 2012: 8
- FWCI
- 21.16
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the Optical Society of America A (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Keywords
- Radon-Wigner transform, fractional Fourier transform, moments, uncertainty relations, signal representation, image processing
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