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Research on resolution between multi-component LFM signals in the fractional Fourier domain

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Abstract

When the initial frequencies and chirp rates of multi-component linear frequency modulation (LFM or chirp) signals are close, the signals may not be distinguished in the fractional Fourier domain (FRFD). Consequently, some signals cannot be detected. In this paper, first, the spectral distribution characteristics of a continuous LFM signal in the FRFD are analyzed, and then the spectral distribution characteristics of a LFM signal in the discrete FRFD are analyzed. Second, the critical resolution distance between the peaks of two LFM signals in the FRFD is deduced, and the relationship between the dimensional normalization parameter and the distance between two LFM signals in the FRFD is also deduced. It is discovered that selecting a proper dimensional normalization parameter can increase the distance. Finally, a method to select the parameter is proposed, which can improve the resolution ability of the fractional Fourier transform (FRFT). Its effectiveness is verified by simulation results.

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References

  1. Tao R, Deng B, Wang Y. Fractional Fourier Transform and its Application (in Chinese). Beijing: Tsinghua University Press, 2009. 1–7

    Google Scholar 

  2. Tao R, Deng B, Wang Y. Research process of the fractional Fourier transform in signal processing. Sci China Ser F-Inf Sci, 2006, 49: 1–25

    Article  MathSciNet  MATH  Google Scholar 

  3. Sun H, Liu G, Gu H, et al. Application of the fractional Fourier transform to moving target detection in airborne SAR. IEEE Trans Aero Elec Sys, 2002, 38: 1416–1424

    Article  Google Scholar 

  4. Zhou G, Ye Z. An approach to estimating the chirp constant of LFM (in Chinese). J Univ Sci Tech China, 2003, 33: 34–38

    Google Scholar 

  5. Zhang B, Liu A, Zhu X, et al. Multicomponent LFM signal detection and parameter estimation based on fractional Fourier transform (in Chinese). J Data Acquis Proces, 2003, 18: 408–411

    Google Scholar 

  6. Zhao X, Tao R, Zhou S, et al. Chirp signal detection and multiple parameter estimation using radon-ambiguity and fractional Fourier transform (in Chinese). Trans Beijing Inst Technol, 2003, 23: 371–374, 377

    Google Scholar 

  7. Qi L, Tao R, Zhou S, et al. Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform. Sci China Ser F-Inf Sci, 2004, 47: 184–198

    Article  MathSciNet  MATH  Google Scholar 

  8. Li J, Wang S, Wang F. Chirp signal analysis based on PWD in fractional Fourier transform domain (in Chinese). Syst Eng Electron, 2005, 27: 988–990, 1015

    Google Scholar 

  9. Sejdić E, Djurović I, Jin J. Time-frequency feature representation using energy concentration: an overview of recent advances. Digit Signal Process, 2009, 19: 153–183

    Article  Google Scholar 

  10. Oonincx P J. Joint time-frequency offset detection using the fractional Fourier transform. Signal Process, 2008, 88: 2936–2942

    Article  MATH  Google Scholar 

  11. Xia X. On Bandlimite signals with fractional Fourier transform. IEEE Signal Proc Let, 1996, 3: 72–74

    Article  Google Scholar 

  12. Deng B, Tao R, Yang X. Analysis of resolution ratio and sample in the fractional Fourier domain. Prog Nat Sci, 2007, 17: 655–661

    Article  Google Scholar 

  13. Liu F, Huang Y, Tao R, et al. Chirp-rate resolution of fractional Fourier transform in multi-component LFM signal. J Beijing Inst Technol, 2009, 18: 74–78

    Google Scholar 

  14. Sharma K K, Joshi S D. Signal separation using linear canonical and fractional Fourier transforms. Opt Commun, 2006, 265: 454–460

    Article  Google Scholar 

  15. Capus C, Brown K. Short-term fractional Fourier methods for the time-frequency representation of chirp signals. J Acoust Soc Am, 2003, 113: 3253–3263

    Article  Google Scholar 

  16. Stankovic L J, Alieva T, Bastiaans M J. Time-frequency signal analysis based on the windowed fractional Fourier transform. Signal Process, 2003, 83: 2459–2468

    Article  MATH  Google Scholar 

  17. Capus C, Brown K. Fractional Fourier transform of the Gaussian and fractional domain signal support. IEE P-Vis Image Sign, 2003, 150: 99–106

    Article  Google Scholar 

  18. Catherall A T, Williams D P. High resolution spectrograms using a component optimized short-term fractional Fourier transform. Signal Process, 2010, 90: 1591–1596

    Article  MATH  Google Scholar 

  19. Amein A S, Soraghan J J. A new chirp scaling algorithm based on the fractional Fourier transform. IEEE Signal Proc Let, 2005, 12: 705–708

    Article  Google Scholar 

  20. Yin Qi, Ni Z, Qian S, et al. Adaptive oriented orthogonal projective decomposition (in Chinese). Acta Electron Sin, 1997, 25: 52–58

    Google Scholar 

  21. Yin Q, Ni Z. A fast implementation of adaptive oriented orthogonal projective decomposition (AOP) (in Chinese). J China Inst Commun, 1998, 19: 22–28

    Google Scholar 

  22. Yin Q, Qian S, Feng A. A fast refinement for adaptive Gaussian chirplet decomposition. IEEE Trans Signal Proces, 2002, 50: 1298–1306

    Article  MathSciNet  Google Scholar 

  23. Almeida L B. The fractional Fourier transform and time-frequency representations. IEEE Trans Signal Proces, 1994, 42: 3084–3091

    Article  Google Scholar 

  24. Ozaktas H M, Arikan O, Kutay M A, et al. Digital computation of the fractional Fourier transform. IEEE Trans Signal Proces, 1996, 44: 2141–2150

    Article  Google Scholar 

  25. Zhao X H, Deng B, Tao R. Practical normalization methods in the digital computation of the fractinal Fourier transform. In: Proceedings of IEEE International Conference on Signal Processing. New York: IEEE Press, 2004. 105–108

    Google Scholar 

  26. Deng B, Tao R, Qu C. Analysis of the shading between multicomponent chirp signals in the fractional Fourier domain (in Chinese). Acta Electron Sin, 2007, 35: 1094–1098

    Google Scholar 

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Authors and Affiliations

  1. Department of Electronic and Information Engineering, Naval Aeronautical Engineering Institute, Yantai, 264001, China

    Feng Liu & HuiFa Xu

  2. The 94362th Unit of People’s Liberation Army, Qingdao, 266111, China

    HuiFa Xu

  3. School of Information Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Ran Tao & Yue Wang

Authors
  1. Feng Liu
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  2. HuiFa Xu
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  3. Ran Tao
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  4. Yue Wang
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Correspondence to HuiFa Xu.

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Liu, F., Xu, H., Tao, R. et al. Research on resolution between multi-component LFM signals in the fractional Fourier domain. Sci. China Inf. Sci. 55, 1301–1312 (2012). https://doi.org/10.1007/s11432-011-4324-6

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  • DOI: https://doi.org/10.1007/s11432-011-4324-6

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