Nonseparable two-dimensional fractional Fourier transform
Open accessAbstract
Previous generalizations of the fractional Fourier transform to two dimensions assumed separable kernels. We present a nonseparable definition for the two-dimensional fractional Fourier transform that includes the separable definition as a special case. Its digital and optical implementations are presented. The usefulness of the nonseparable transform is justified with an image-restoration example.
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The continuous fractional Fourier transform kernel has a spectral expansion in terms of Hermite-Gaussian functions.
“The kernel is known to have the following spectral expansion [3]:”
From The discrete fractional Fourier transform (2000) · cites this paper as [3]
The Introduction (page unavailable) gives an exponential-form kernel for the continuous fractional Fourier transform, but does not give a spectral expansion. Searches for Hermite-Gaussian functions, eigenfunctions, and spectral expansion found no passage establishing the attributed claim. (LLM, conf=0.72)
Experimental — accuracy not yet measuredNamias reached the integral kernel of the FRT from its spectral expansion using certain identities and formulas for the Hermite-Gaussian functions [3].
“It was later noticed that Namias had reached the integral kernel of the FRT from its spectral expansion using certain identities and formulas for the Hermite-Gaussian functions [3].”
From The discrete fractional Fourier transform (2000) · cites this paper as [3]
The Introduction gives an integral kernel for the fractional Fourier transform, but does not say how Namias obtained it. Searches for Namias, spectral expansion, and Hermite-Gaussian functions found no passage in our copy describing the claimed derivation; the References only list a work about Namias's transform. (LLM, conf=0.70)
Experimental — accuracy not yet measured
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Flagged first, then by citations
Research works printed but not linked: 1
- [24]24. A. Sahin, "Two-dimensional fractional Fourier transform and its optical implementation," M.S. thesis ͑Bilkent University, Ankara, Turkey, 1996͒.
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Sorted by citations
The discrete fractional Fourier transform
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Self-citationThe discrete fractional Fourier transform
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Self-citation
- Authors
- Sahin, A., Kutay, M. A., & Ozaktas, H. M.
- Affiliations
- Bilkent University (TR)
- ORCID
- Kutay, M. Alper
- Venue
- Applied Optics
- Publisher
- Optica Publishing Group
- Published
- 1998-08-10
- Volume
- 37
- Issue
- 23
- Pages
- 5444
- ISSN
- 0003-6935 (ISSN-L)
- 1539-4522
- OpenAlex
- W2105167631
- Semantic Scholar
- d1d9309ff713fda932658e79937ca0449dde3420
- Cited by
- 41
- References
- 37
- Citations by year
- 2026: 4 · 2025: 3 · 2023: 1 · 2020: 2 · 2019: 1 · 2018: 3 · 2017: 1 · 2016: 2 · 2015: 3 · 2014: 3 · 2012: 1
- FWCI
- 4.97
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Locations
- Applied Optics (publishedVersion)
- PubMed (publishedVersion)
- Bilkent University Institutional Repository (Bilkent University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Image Processing Techniques
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Keywords
- separable kernels, digital implementation, optical implementation, image restoration
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