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Journal articles on the topic 'Fractional Fourier transform'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Zakia, Abdul Wahid, Iqbal Saleem, Sarwar Farhana, and Rehman Abdul. "THEKERNEL OF N- DIMENSIONAL FRACTIONAL FOURIER TRANSFORM." International Journal of Engineering Technologies and Management Research 7, no. 1 (2020): 36–41. https://doi.org/10.5281/zenodo.3707069.

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In this paper we have developed the kernel of N-dimensional fractional Fourier transform by extending the definition of first dimensional fractional Fourier transform. The properties of kernel up to N- dimensional are also presented here which is missing in the literature of fractional Fourier transform. The properties of kernel of fractional Fourier transforms up to N- dimensional will help the researcher to extend their research in this aspect.

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2

Wahid, Zakia Abdul, Saleem Iqbal, Farhana Sarwar, and Abdul Rehman. "THEKERNEL OF N- DIMENSIONAL FRACTIONAL FOURIER TRANSFORM." International Journal of Engineering Technologies and Management Research 7, no. 1 (2020): 36–41. http://dx.doi.org/10.29121/ijetmr.v7.i1.2020.495.

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In this paper we have developed the kernel of N-dimensional fractional Fourier transform by extending the definition of first dimensional fractional Fourier transform. The properties of kernel up to N- dimensional are also presented here which is missing in the literature of fractional Fourier transform. The properties of kernel of fractional Fourier transforms up to N- dimensional will help the researcher to extend their research in this aspect.

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3

Majorkowska-Mech, Dorota, and Aleksandr Cariow. "Discrete Pseudo-Fractional Fourier Transform and Its Fast Algorithm." Electronics 10, no. 17 (2021): 2145. http://dx.doi.org/10.3390/electronics10172145.

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In this article, we introduce a new discrete fractional transform for data sequences whose size is a composite number. The main kernels of the introduced transform are small-size discrete fractional Fourier transforms. Since the introduced transformation is not, in the generally known sense, a classical discrete fractional transform, we call it discrete pseudo-fractional Fourier transform. We also provide a generalization of this new transform, which depends on many fractional parameters. A fast algorithm for computing the introduced transform is developed and described.

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4

Atakishiyev, Natig M., and Kurt Bernardo Wolf. "Fractional Fourier–Kravchuk transform." Journal of the Optical Society of America A 14, no. 7 (1997): 1467. http://dx.doi.org/10.1364/josaa.14.001467.

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5

Khare, Kedar, and Nicholas George. "Fractional finite Fourier transform." Journal of the Optical Society of America A 21, no. 7 (2004): 1179. http://dx.doi.org/10.1364/josaa.21.001179.

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6

Liu, Zhengjun, and Shutian Liu. "Random fractional Fourier transform." Optics Letters 32, no. 15 (2007): 2088. http://dx.doi.org/10.1364/ol.32.002088.

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7

SUTRISNA, IIN, Asriadi Nasrun, Mawardi Bahri, and Syamsuddin Toaha. "Transformasi Fourier Fraksional dari Fungsi Gaussian." Jurnal Matematika, Statistika dan Komputasi 16, no. 1 (2019): 19. http://dx.doi.org/10.20956/jmsk.v16i1.5939.

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The fractional Fourier transform is one of the generalizations of ordinary Fourier transform that depend on a particular angle . In this paper we will derive the fractional Fourier transforms of a function that is well known in the field of analysis, namely Gaussian function.

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8

Jin, Jian Guo, Chen Chen, Ming Jun Wei, and Li Chun Xia. "Research of FRFT Rotation Factor Sensitivity and Diffusion Based on Audio." Applied Mechanics and Materials 155-156 (February 2012): 337–41. http://dx.doi.org/10.4028/www.scientific.net/amm.155-156.337.

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As the fractional Fourier transform has advantages in signal processing areas, it has been used more and more in various fields. Based on audio data sources, the paper analyzed the rotation factor sensitivity and diffusion of fractional Fourier transform. System test results show that the fractional Fourier transforms rotation factor sensitivity Δα≥10-3. It plays an important role in the area of attacking chaos. Diffusion analysis shows that it will lead to the complete failure of inverse transform to restore the original signal, when any element cn of fractional Fourier domain changes 0.2 tim

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9

Wei, Cheng-Dong, and Guang-Sheng Chen. "Application of local fractional fourier sine transform for 1-D local fractional heat transfer equation." Thermal Science 22, no. 4 (2018): 1729–35. http://dx.doi.org/10.2298/tsci1804729w.

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This paper proposes a new method called the local fractional Fourier sine transform to solve fractional differential equations on a fractal space. The method takes full advantages of the Yang-Fourier transform, the local fractional Fourier cosine, and sine transforms. A 1-D local fractional heat transfer equation is used as an example to reveal the merits of the new technology, and the example can be used as a paradigm for other applications.

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10

Seok, Jongwon, Taehwan Kim, and Keunsung Bae. "LFM Signal Separation Using Fractional Fourier Transform." Journal of the Korean Institute of Information and Communication Engineering 17, no. 3 (2013): 540–45. http://dx.doi.org/10.6109/jkiice.2013.17.3.540.

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11

Bahri, Mawardi, and Samsul Ariffin Abdul Karim. "Fractional Fourier Transform: Main Properties and Inequalities." Mathematics 11, no. 5 (2023): 1234. http://dx.doi.org/10.3390/math11051234.

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The fractional Fourier transform is a natural generalization of the Fourier transform. In this work, we recall the definition of the fractional Fourier transform and its relation to the conventional Fourier transform. We exhibit that this relation permits one to obtain easily the main properties of the fractional Fourier transform. We investigate the sharp Hausdorff-Young inequality for the fractional Fourier transform and utilize it to build Matolcsi-Szücs inequality related to this transform. The other versions of the inequalities concerning the fractional Fourier transform is also discussed

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12

Khudair, Ayad R. "Random Fractional Laplace Transform for Solving Random Time-Fractional Heat Equation in an Infinite Medium." BASRA JOURNAL OF SCIENCE 38, no. 2 (2020): 223–47. http://dx.doi.org/10.29072/basjs.202025.

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The random Laplace and Fourier transforms are very important tools to solve random heat problems. Unfortunately, it is difficult to use these random integral transforms for solving the fractional random heat problems, where the mean square conformable fractional derivative is used to express for the time fractional derivative. Therefore, this work adopts the extension of the random Laplace transform into random fractional Laplace transform in order to solve this kind of heat problems. The stochastic process solution of the fractional random heat in an infinite medium is investigated by using r

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13

Xu, Hui Yan. "Fractional Fourier Transform Image Analysis." Applied Mechanics and Materials 198-199 (September 2012): 288–93. http://dx.doi.org/10.4028/www.scientific.net/amm.198-199.288.

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As a generalized form of the Fourier transform, fractional Fourier transform (FRFT) ,which is integrated the signal in time domain and frequency domain, is a new time-frequency analysis. From the simulation point of view to image the distribution of energy in the fractional Fourier domain, the amplitude and phase characteristics, simulation results show that any fractional Fourier domain, can reflect the image of the space-frequency domain characteristics, with the order, the image The distribution of the space-frequency domain characteristics will change. The image of the fractional Fourier t

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14

Zhao, Tieyu, Tianyu Yang, and Yingying Chi. "Quantum Weighted Fractional Fourier Transform." Mathematics 10, no. 11 (2022): 1896. http://dx.doi.org/10.3390/math10111896.

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Quantum Fourier transform (QFT) is an important part of many quantum algorithms. However, there are few reports on quantum fractional Fourier transform (QFRFT). The main reason is that the definitions of fractional Fourier transform (FRFT) are diverse, while some definitions do not include unitarity, which leads to some studies pointing out that there is no QFRFT. In this paper, we first present a reformulation of the weighted fractional Fourier transform (WFRFT) and prove its unitarity, thereby proposing a quantum weighted fractional Fourier transform (QWFRFT). The proposal of QWFRFT provides

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15

Sharma, Vidya, and Akash Patalwanshi. "Convolution Structure of the Fractional Fourier-Laplace Transform." International Journal of Science and Research (IJSR) 13, no. 8 (2024): 1599–602. http://dx.doi.org/10.21275/mr24827135434.

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16

Sharma, Vidya, and Akash Patalwanshi. "Operational Calculus for the Fractional Fourier-Laplace Transform." International Journal of Science and Research (IJSR) 14, no. 1 (2025): 853–62. https://doi.org/10.21275/sr25119122327.

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17

Wu, Jiasong, Fuzhi Wu, Qihan Yang, et al. "Fractional Spectral Graph Wavelets and Their Applications." Mathematical Problems in Engineering 2020 (November 6, 2020): 1–18. http://dx.doi.org/10.1155/2020/2568179.

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One of the key challenges in the area of signal processing on graphs is to design transforms and dictionary methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier transform (GFT) to spectral graph fractional Fourier transform (SGFRFT), which is then used to define a novel transform named spectral graph fractional wavelet transform (SGFRWT), which is a generalized and extended version of spectral graph wavelet transform (SGWT). A fast algorithm for SGFRWT is also derived and implemented based on Fourier series approximation. Som

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18

V., D. Sharma* P. B. Deshmukh. "CONVOLUTION STRUCTURE OF FRACTIONAL QUATERNION FOURIER TRANSFORM." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 5, no. 10 (2016): 176–82. https://doi.org/10.5281/zenodo.159348.

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The quaternion are a number system that extends the complex numbers. It uses in theoretical and applied branch of mathematics. The main applications of quaternion are filter design and color image processing. It has vital role in animation field. The aim of our work is the convolution structure of Fractional Quaternion Fourier Transform is given which is useful in image processing. Also we have proved some basic properties like associative, distributive, linear, shifting for the convolution of Fractional Quaternion Fourier Transform.

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19

Pellat-Finet, Pierre, and Georges Bonnet. "Fractional order Fourier transform and Fourier optics." Optics Communications 111, no. 1-2 (1994): 141–54. http://dx.doi.org/10.1016/0030-4018(94)90154-6.

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20

Zhong, Wei Ping, Feng Gao, and Xiao Ming Shen. "Applications of Yang-Fourier Transform to Local Fractional Equations with Local Fractional Derivative and Local Fractional Integral." Advanced Materials Research 461 (February 2012): 306–10. http://dx.doi.org/10.4028/www.scientific.net/amr.461.306.

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Yang-Fourier transform is the generalization of the fractional Fourier transform of non-differential functions on fractal space. In this paper, we show applications of Yang-Fourier transform to local fractional equations with local fractional derivative and local fractional integral

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21

Seok, Jongwon, Taehwan Kim, and Geon-Seong Bae. "Active Sonar Target Recognition Using Fractional Fourier Transform." Journal of the Korea Institute of Information and Communication Engineering 17, no. 11 (2013): 2505–11. http://dx.doi.org/10.6109/jkiice.2013.17.11.2505.

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22

García, Javier, David Mas, and Rainer G. Dorsch. "Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm." Applied Optics 35, no. 35 (1996): 7013. http://dx.doi.org/10.1364/ao.35.007013.

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23

Jin, Sang-il, and Soo-Young Lee. "Joint transform correlator with fractional Fourier transform." Optics Communications 207, no. 1-6 (2002): 161–68. http://dx.doi.org/10.1016/s0030-4018(02)01499-2.

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24

Prasad, Akhilesh, Praveen Kumar, and Tanuj Kumar. "Product of continuous fractional wave packet transforms." International Journal of Wavelets, Multiresolution and Information Processing 17, no. 04 (2019): 1950021. http://dx.doi.org/10.1142/s0219691319500218.

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In this paper, we investigated the fractional Fourier transform (FrFT) of the continuous fractional wave packet transform and studied some properties of continuous fractional wave packet transform. The product of continuous fractional wave packet transforms (CFrWPTs) is defined. Parseval’s relation and an inversion formula for product of CFrWPT are obtained. An example is also given.

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25

Shubham, D. Shedge, and N. Bhosale Bharat. "Modulation And Parseval's Theorem For Wavelet Transform As An Extension Of Fractional Fourier Transform." International Journal of Advance and Applied Research 10, no. 3 (2023): 271 to 275. https://doi.org/10.5281/zenodo.7678164.

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<em>Integral transforms have been wide use to solve various ordinary and partial differential equations or problems in pure and applied mathematics. Wavelet Transform and Fractional Fourier transform has many applications in signal and image processing. </em> <em>             This paper describes the scaling, modulation and Parseval’s theorem of Wavelet Transform as an extension of Fractional Fourier transform.</em>

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26

Hong-Yi, Fan, and Jiang Nian-Quan. "From Complex Fractional Fourier Transform to Complex Fractional Radon Transform." Communications in Theoretical Physics 42, no. 1 (2004): 23–26. http://dx.doi.org/10.1088/0253-6102/42/1/23.

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27

S.B. Gaikwad, S. B. Gaikwad. "Fractional Fourier Transform of Boehmians." IOSR Journal of Mathematics 5, no. 3 (2013): 57–69. http://dx.doi.org/10.9790/5728-0535769.

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28

Lohmann, Adolf W., and David Mendlovic. "Fractional fourier transform: photonic implementation." Applied Optics 33, no. 32 (1994): 7661. http://dx.doi.org/10.1364/ao.33.007661.

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29

Saxena, Rajiv, and Kulbir Singh. "Fractional Fourier Transform: A Review." IETE Journal of Education 48, no. 1 (2007): 13–29. http://dx.doi.org/10.1080/09747338.2007.11657862.

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30

Candan, C., M. A. Kutay, and H. M. Ozaktas. "The discrete fractional Fourier transform." IEEE Transactions on Signal Processing 48, no. 5 (2000): 1329–37. http://dx.doi.org/10.1109/78.839980.

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31

Pei, Soo-Chang, and Min-Hung Yeh. "Improved discrete fractional Fourier transform." Optics Letters 22, no. 14 (1997): 1047. http://dx.doi.org/10.1364/ol.22.001047.

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32

Cai, Yangjian, Qiang Lin, and Shi-Yao Zhu. "Coincidence subwavelength fractional Fourier transform." Journal of the Optical Society of America A 23, no. 4 (2006): 835. http://dx.doi.org/10.1364/josaa.23.000835.

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33

Song, Jun, Rui He, Hao Yuan, Jun Zhou, and Hong-Yi Fan. "Joint Wavelet—Fractional Fourier Transform." Chinese Physics Letters 33, no. 11 (2016): 110302. http://dx.doi.org/10.1088/0256-307x/33/11/110302.

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34

De Bie, Hendrik, and Nele De Schepper. "The Fractional Clifford-Fourier Transform." Complex Analysis and Operator Theory 6, no. 5 (2012): 1047–67. http://dx.doi.org/10.1007/s11785-012-0229-7.

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35

Feng Zhang, Yan Qiu Chen, and Guoan Bi. "Adaptive harmonic fractional Fourier transform." IEEE Signal Processing Letters 6, no. 11 (1999): 281–83. http://dx.doi.org/10.1109/97.796288.

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36

Alieva, T., and M. J. Bastiaans. "On fractional Fourier transform moments." IEEE Signal Processing Letters 7, no. 11 (2000): 320–23. http://dx.doi.org/10.1109/97.873570.

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37

Soo-Chang Pei and Wen-Liang Hsue. "Random Discrete Fractional Fourier Transform." IEEE Signal Processing Letters 16, no. 12 (2009): 1015–18. http://dx.doi.org/10.1109/lsp.2009.2027646.

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38

Singer, Peter. "An integrated fractional Fourier transform." Journal of Computational and Applied Mathematics 54, no. 2 (1994): 221–37. http://dx.doi.org/10.1016/0377-0427(94)90178-3.

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39

Sahbani, Samir. "Fractional Fourier–Jacobi type transform." ANNALI DELL'UNIVERSITA' DI FERRARA 66, no. 1 (2020): 135–56. http://dx.doi.org/10.1007/s11565-020-00337-3.

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40

Çenesiz, Yücel, and Ali Kurt. "The solutions of time and space conformable fractional heat equations with conformable Fourier transform." Acta Universitatis Sapientiae, Mathematica 7, no. 2 (2015): 130–40. http://dx.doi.org/10.1515/ausm-2015-0009.

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Abstract In this paper our aim is to find the solutions of time and space fractional heat differential equations by using new definition of fractional derivative called conformable fractional derivative. Also based on conformable fractional derivative definition conformable Fourier Transform is defined. Fourier sine and Fourier cosine transform definitions are given and space fractional heat equation is solved by conformable Fourier transform.

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41

Zhang, Xindan, and Haoyuan Zheng. "Signal Enhancement Methods Based on Wavelet Transform, Fractional Fourier Transform and Short-time Fourier Transform." Highlights in Science, Engineering and Technology 76 (December 31, 2023): 222–30. http://dx.doi.org/10.54097/eyfndn07.

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This review paper mainly focuses on different signal enhancement methods such as wavelet transform, fractional Fourier transform (FrFT) and short-time Fourier transform (STFT). First, this paper introduces the concept and importance of signal enhancement, as well as some current issues and challenges. Then, in recent years, the application of the three methods in wavelet transform, fractional Fourier transform and short-time Fourier transform is described. In terms of wavelet transform, this paper discusses the application of wavelet function to image enhancement and the specific steps, and an

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42

Vilardy O., Juan M., Ronal A. Perez, and Cesar O. Torres M. "Optical Image Encryption Using a Nonlinear Joint Transform Correlator and the Collins Diffraction Transform." Photonics 6, no. 4 (2019): 115. http://dx.doi.org/10.3390/photonics6040115.

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The Collins diffraction transform (CDT) describes the optical wave diffraction from the generic paraxial optical system. The CDT has as special cases the diffraction domains given by the Fourier, Fresnel and fractional Fourier transforms. In this paper, we propose to describe the optical double random phase encoding (DRPE) using a nonlinear joint transform correlator (JTC) and the CDT. This new description of the nonlinear JTC-based encryption system using the CDT covers several optical processing domains, such as Fourier, Fresnel, fractional Fourier, extended fractional Fourier and Gyrator do

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43

Dai, Zhi Ping, Zhen Feng Yang, Zhen Jun Yang, Zhao Guang Pang, and Shu Min Zhang. "Numerical Simulation of Anomalous Vortex Beams on Different Fractional Fourier Transform Planes." Applied Mechanics and Materials 556-562 (May 2014): 3745–48. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.3745.

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The properties of fractional Fourier transform of anomalous vortex beams are studied. A new type of analytical expression of fractional Fourier transform for anomolous vortex beams is obtained. The properties of anomolous vortex beams on different fractional Fourier transform planes with different parameters are illustrated. The results show that the anomolous vortex beams always has a doughnut profile, the distribution of intensity on different fractional Fourier transform planes highly depends on the fractional order and the beam parameters, such as the beam order and the topological charge.

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44

Zhao, Tieyu, and Yingying Chi. "Multiweighted-Type Fractional Fourier Transform: Unitarity." Fractal and Fractional 5, no. 4 (2021): 205. http://dx.doi.org/10.3390/fractalfract5040205.

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The definition of the discrete fractional Fourier transform (DFRFT) varies, and the multiweighted-type fractional Fourier transform (M-WFRFT) is its extended definition. It is not easy to prove its unitarity. We use the weighted-type fractional Fourier transform, fractional-order matrix and eigendecomposition-type fractional Fourier transform as basic functions to prove and discuss the unitarity. Thanks to the growing body of research, we found that the effective weighting term of the M-WFRFT is only four terms, none of which are extended to M terms, as described in the definition. Furthermore

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45

Wang, Zhuoran. "Review on application of fractional Fourier transform in LinearFrequencyModulation signal and communication system." Theoretical and Natural Science 41, no. 1 (2024): 100–107. http://dx.doi.org/10.54254/2753-8818/41/20240504.

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Traditional Fourier transform often apply to analyze and process stationary signals, however, it is weak for time-varying non-stationary signals, and fractional Fourier transform (FRFT) can better solve such problems. The FRFT can be comprehended as the expressive methods on the fractional Fourier domain constituted by the spinning coordinate axis of the signal anticlockwise about the origin at arbitrarily Angle in the time-frequency plane. In this paper, the improved fractional Fourier transform is combined with other calculation methods to achieve high precision estimation of chirp signal pa

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46

Mustard, David. "Uncertainty principles invariant under the fractional Fourier transform." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 33, no. 2 (1991): 180–91. http://dx.doi.org/10.1017/s0334270000006986.

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AbstractUncertainty principles like Heisenberg's assert an inequality obeyed by some measure of joint uncertainty associated with a function and its Fourier transform. The more groups under which that measure is invariant, the more that measure represents an intrinsic property of the underlying object represented by the given function. The Fourier transform is imbedded in a continuous group of operators, the fractional Fourier transforms, but the Heisenberg measure of overall spread turns out not to be invariant under that group. A new family is developed of measures that are invariant under t

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47

Kamalakkannan, Ramanathan, Rajakumar Roopkumar, and Ahmed Zayed. "Short time coupled fractional fourier transform and the uncertainty principle." Fractional Calculus and Applied Analysis 24, no. 3 (2021): 667–88. http://dx.doi.org/10.1515/fca-2021-0029.

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Abstract In this paper, we introduce a short-time coupled fractional Fourier transform (scfrft) using the kernel of the coupled fractional Fourier transform (cfrft). We then prove that it satisfies Parseval’s relation, derive its inversion and addition formulas, and characterize its range on ℒ 2(ℝ2). We also study its time delay and frequency shift properties and conclude the article by a derivation of an uncertainty principle for both the coupled fractional Fourier transform and short-time coupled fractional Fourier transform.

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48

Protsenko, M. A., and E. A. Pavelyeva. "FRACTIONAL WAVELET TRANSFORM PHASE FOR IRIS IMAGE KEY POINTS MATCHING." International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLVIII-2/W3-2023 (May 12, 2023): 201–7. http://dx.doi.org/10.5194/isprs-archives-xlviii-2-w3-2023-201-2023.

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Abstract. In this article the fractional phase congruency method for iris image key points descriptors is proposed. The fractional phase congruency is calculated using fractional wavelet transform through the fractional Fourier transform. Fractional Fourier transform is the generalization of the classical Fourier transform. The use of fractional phase congruency can achieve better results compared to the use of the classical phase congruency. The comparison between phase congruency and fractional phase congruency for biometric iris images is given. The optimal parameters of fractional wavelet

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49

Wu, Guang Zhi, Gang Fu, and Yan Jun Wu. "Detection and Parameter Estimation of Chirp Signal Based on Time-Frequency Analysis." Advanced Materials Research 989-994 (July 2014): 3989–92. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.3989.

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Based on the relationship between the Radon-Wigner transform and fractional Fourier transform and the time frequency distribution, using the property that Radon-Wigner transform has better performance in time and frequency domain, detection and parameter estimation of Chirp signal have been done by Radon-Wigner transform or fractiona1 Fourier transform. The theoretica1 analysis and simulation prove that two techniques are better than generic time-frequency transform, such as Wigner-Ville transform.

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50

Zhao, Zhengang, and Yi Gong. "Modified Fourier Sine and Cosine transforms for the Hadamard fractional calculus." Journal of Physics: Conference Series 2905, no. 1 (2024): 012016. https://doi.org/10.1088/1742-6596/2905/1/012016.

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Abstract Nowadays, the study of Hadamard fractional calculus is a hot topic, where the Hadamard fractional calculus is more suitable for describing the very slow process. Due to the logarithmic integral kernel of Hadamard calculus, it brings great difficulties to the corresponding theoretical analysis and numerical calculation. In this research, we introduce a novel modified Fourier Sine transform and a Fourier Cosine transform and then study the corresponding convolution theorem for the Fourier Sine and Cosine transforms. Finally, we provide the transformation results of the Hadamard fraction

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