Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 42, 24 June 2024
Open
Access | Article
Fractional fourier transform and its application
* Author to whom correspondence should be addressed.
Abstract
The Fourier Transform (FT) is a linear transformation for the primitive function. It takes some set of functions to be an orthogonal basis. Its physical meaning is to transfer the primitive function onto each set of base functions. Because it can convert functions between the time and frequency domains, the FT is widely employed in many fields. The Fractional Fourier Transform (FrFT) is an improvement and progress based on the FT. This paper will define the FT and FrFT. Then the distinction between FrFT and FT is discussed. Finally, specific examples of its application in processing digital image are provided. FrFT is the process of transforming an image function into a series of periodic functions. The FrFT is used as a powerful mathematical tool to understand non- smooth signals, nonlinear systems and complicated phenomena, which is significant and has broad possibilities in the fields of signal processing, communication, image processing, optical imaging and quantum information processing.
Keywords
Fourier Transform; Fractional Fourier Transform; Decentralized image resoration; Face recognition
References
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2. Xia, Y. (2023) SAR image ship wake detection based on FT[J]. Ship Science and Technology, 45, 186-189.
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4. Sun, J. (2011) Research on FT in textile images[J]. Modern Electronic Technology, 34, 97-98.
5. Zhao, K., Li, Q. and Xuan, Y. (2008) Reconstruction method for three-dimensional porous media based on image processing and FT[J]. Journal of Engineering Thermophysics, 2, 287-290.
6. Liu, H., Guo, B. and Feng, Z. (2006) Remote sensing image alignment based on FT[J]. Optoelectronics-Laser, 11, 1393-1397.
7. Ozaktas, H. M., Zalevsky, Z. and Kutay, M.A., (2000) The FrFT with Applications in Optics and Signal Processing [M]. New York, Wiley.
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Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of Machine Learning: Integrating machine learning techniques to advance network security - CONFMPCS 2024
- ISBN (Print)
- 978-1-83558-495-8
- ISBN (Online)
- 978-1-83558-496-5
- Published Date
- 24 June 2024
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/42/20240103
- Copyright
- 24 June 2024
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited