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Fractional Fourier transformation and its application on optical communication

  • TANG Ming ,
  • YANG Aiying ,
  • XIN Xiangjun
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  • 1. National Engineering Laboratory for Next Generation Internet Access System;School of Optics and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China;
    2. School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China;
    3. School of Electrical Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received date: 2016-06-30

  Revised date: 2016-07-18

  Online published: 2016-09-21

Abstract

Fractional Fourier transformation (FrFT) is an extension form of the Fourier transformation (FT). It can analyze the fractional signal between time and frequency domains. Thanks to its unique properties, the FrFT has found multiple applications such as solving differential equations, quantum mechanics, optical image processing and signal processing. This paper gives a brief introduction to FrFT and reviews the current research progress of FrFT in several fields such as filtering, neural network, image processing and wireless communication. In addition, some typical applications in optical communication are depicted in detail. Some research directions of FrFT in optical communication field are suggested.

Cite this article

TANG Ming , YANG Aiying , XIN Xiangjun . Fractional Fourier transformation and its application on optical communication[J]. Science & Technology Review, 2016 , 34(16) : 139 -143 . DOI: 10.3981/j.issn.1000-7857.2016.16.017

References

[1] Namias V. The fractional order fourier transform and its application to quantum mechanics[J]. Geoderma, 2012, 25(3):236-242.
[2] Mendlovic D, Ozaktas H M. Fractional Fourier transforms and their optical implementation:I[J]. Journal of the Optical Society of America A optics & Image Science, 1993, 10(9):1875-1881.
[3] Sahin A, Ozaktas H M, Mendlovic D. Fractional Fourier transforms and their optical implementation. Ⅱ[J]. Journal of the Optical Society of America A optics & Image Science, 1993, 10(12):2522-2531.
[4] Lohmann A W. Image rotation, Wigner rotation, and the fractional fourier transform[J]. Journal of the Optical Society of America A, 1993, 10(10):2181-2186.
[5] Almeida L B. The fractional Fourier transform and time-frequency representations[J]. IEEE Transactions on Signal Processing, 1994, 42(11):3084-3091.
[6] Lang J, Tao R, Ran Q W, et al. Short-time fractional Fourier transform and its applications[J]. IEEE Transactions on Signal Processing, 2010, 58(5):2568-2580.
[7] Shi J, Zhang N T, Liu X P. A novel fractional wavelet transforms and its applications[J]. Science China Information Sciences, 2012, 55(6):1270-1279.
[8] 董永强, 陶然, 周思永, 等. 含未知参数的多分量Chirp信号的分数阶傅里叶分析[J]. 北京理工大学学报, 1999, 19(5):612-616. Dong Yongqiang, Tao Ran, Zhou Siyong, et al. The fractional fourier analysis of multicomponent chirp signals with unknown parameters[J]. Journal of Beijing Institute of Technology, 1999, 19(5):612-616.
[9] Lin Q, Ran T, Zhou S, et al. Detection and parameter estimation of multicomponent LFM signal based on the fractional fourier transform[J]. Science in China, 2004, 47(2):184-198.
[10] Akay O, Boudreaux-Bartels G F. Fractional convolution and correlation via operator methods and an application to detection of linear FM signals[J]. IEEE Transactions on Signal Processing, 2001, 49(5):979-993.
[11] 邓兵, 陶然, 齐林, 等. 分数阶Fourier变换与时频滤波[J]. 系统工程与电子技术, 2004, 26(10):1357-1359. Deng Bin, Tao Ran, Qi Lin, et al. Fractional Fourier transform and time-frequency filtering[J]. Systems Engineering and Electronics, 2004, 26(10):1357-1359.[12 Erden M F, Kutay M A, Ozaktas H M. Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration[J]. IEEE Transactions on Signal Processing, 1999, 47(5):1458-1462.
[13] Djurovic I, Stankovic S, Pitas I. Digital watermarking in the fractional Fourier transformation domain[J]. Journal of Network & Computer Applications, 2001, 24(2):167-173.
[14] Shin S G, Jin S I, Shin S Y, et al. Optical neural network using fractional Fourier transform, log-likelihood, and parallelism[J]. Optics Communications,1998, 153:218-222.
[15] Barshan B, Ayrulu B. Fractional Fourier transform pre-processing for neural networks and its application to object recognition[J]. Neural Networks, 2002, 15(1):131-140.
[16] Samil Yetik I, Nehorai A. Beamforming using the fractional Fourier transform[J]. Signal Processing IEEE Transactions on, 2003, 51(6):1663-1668.
[17] 陶然, 周云松. 基于分数阶傅里叶变换的宽带LFM信号波达方向估计新算法[J]. 北京理工大学学报, 2005, 25(10):895-899. Tao Ran, Zhou Yunsong. A novel method for the direction of arrival estimation ofwideband linear frequency modulated sources basedon fractional Fourier transform[J]. Transactions of Beijing Institute of Technology, 2005, 25(10):895-899.
[18] 陈恩庆, 陶然, 张卫强. 一种基于分数阶傅立叶变换的时变信道参数估计方法[J]. 电子学报, 2006, 33(12):2101-2104. Chen Enqing, Tao Ran, Zhang Weiqiang. A method for time-varying channel parameter estimationbased on fractional Fourier transform[J]. Acta Electronica Sinica, 2006, 33(12):2101-2104.
[19] Martone M. A multicarrier system based on the fractional Fourier transform for time-frequency-selective channels[J]. IEEE Transactions on Communications, 2001, 49(6):1011-1020.
[20] 殷敬伟, 惠俊英, 蔡平, 等. 基于分数阶Fourier变换的水声信道参数估计[J]. 系统工程与电子技术, 2007, 29(10):1624-1627. Ying Jingwei, Hui Junying, Cai Pin, et al. Underwater acoustic channel parameter estimationbased on fractional Fourier transforms[J]. Systems Engineering and Electronics, 2007, 29(10):1624-1627.
[21] Cheng H, Li W, Fan Y, et al. A novel fiber nonlinearity suppression method in DWDM optical fiber transmission systems with an all-optical predistortion module[J]. Optics Communications, 2013, 290(290):152-157.
[22] Han Q, Li W, Yang M. An optical waveform pre-distortion method based on time domain fractional Fourier transformation[J]. Optics Communications, 2011, 284(2):660-664.
[23] Zhou H, Li B, Tang M, et al. A fast and robust blind chromatic dispersion estimation based on fractional fourier transformation[C]//European Conference on Optical Communication, 2015. Valencia:IEEE, 2015:1-3.
[24] 杨爱英, 陈晓宇. 分数阶傅里叶变换测量光纤链路色散的方法:201410752087.8[P]. 2015-03-25. Yang Aiying, Chen Xiaoyu. A method based on fractional Fourier transformation for measuring chromatic along a fiber link:201410752087.8[P]. 2015-03-25.
[25] Deng L, Cheng M, Wang X, et al. Secure OFDM-PON system based on chaos and fractional Fourier transform techniques[J]. Journal of Lightwave Technology, 2014, 32(15):2629-2635.
[26] Zhou H, Wu J, Tang M, et al. Joint timing and frequency synchronization based on FrFT encoded training symbol for coherent optical OFDM systems[C]. Optical Fiber Communication Conference (OFC) 2016, Anaheim, California, March 20-22, 2016.
[27] Gabriella C. What else can an AWG do?[J]. Optics Express, 2012, 20(26):1-3.
[28] Curzon G, Kantamaneni B D, Winch J, et al. Optical OFDM based on the fractional Fourier transform[C]//International Conference on Transparent Optical Networks. Coventry:IEEE, 2012:1-4.
[29] Nagashima T, Cincotti G, Murakawa T, et al. PAPR management of all-optical OFDM signal using fractional fourier transform for fibre nonlinearity mitigation[C]//Optical Communication (ECOC), 2015 European Conference on. Valencia:IEEE, 2015. Doi:10.1109/ECOC.2015.7341785.
[30] Konishi T, Murakawa T, Nagashima T, et al. Flexible OFDM-based access systems with intrinsic function of chromatic dispersion compensation[J]. Optical Fiber Technology, 2015, 26:94-99.
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