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Singularity power spectrum distribution

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  • Xiong, Gang
  • Yu, Wenxian
  • Zhang, Shuning

Abstract

Fractal and multifractal signal processing are hot topics in current studies. At present, the research mainly concentrates in fractal dimension, multifractal spectrum and time-singularity spectrum distribution, which are based on differentiability of fractal subsets, however fail to reflect the energy and power measurement of fractal singular subset. Therefore, singularity power spectrum distribution (SPSD) is proposed in this paper, based on the traditional power spectrum density function and multifractal spectrum. In theory, basic concept of SPSD is put forward based on the related singularity measure, the theoretical expression of SPSD is deduced, and the compatibility between SPSD and conventional power spectrum analysis is proved. In algorithm, the discrete approximation algorithm of SPSD for discrete fractal time series is introduced. Simulation based on the multifractal Brownian motion (mFBM) and actual sea clutter indicates that SPSD can reveal effectively the singular power distribution of sea clutter and mFBM, and identify fractal signals, even for those with approximate multifractal spectra or approximate power spectra. The SPSD will provide application prospect of multifractal signal processing, detection and distinguishing of multifractal time series.

Suggested Citation

  • Xiong, Gang & Yu, Wenxian & Zhang, Shuning, 2015. "Singularity power spectrum distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 63-73.
    • Handle: RePEc:eee:phsmap:v:431:y:2015:i:c:p:63-73
    DOI: 10.1016/j.physa.2015.02.025
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    References listed on IDEAS

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    1. Xiong, Gang & Zhang, Shuning & Yang, Xiaoniu, 2012. "The fractal energy measurement and the singularity energy spectrum analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6347-6361.
    2. B. Lashermes & S. G. Roux & P. Abry & S. Jaffard, 2008. "Comprehensive multifractal analysis of turbulent velocity using the wavelet leaders," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(2), pages 201-215, January.
    3. Amir Bashan & Ronny Bartsch & Jan W. Kantelhardt & Shlomo Havlin, 2008. "Comparison of detrending methods for fluctuation analysis," Papers 0804.4081, arXiv.org.
    4. Alvarez-Ramirez, Jose & Rodriguez, Eduardo & Carlos Echeverría, Juan, 2005. "Detrending fluctuation analysis based on moving average filtering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 199-219.
    5. Castro e Silva, A. & Moreira, J.G., 1997. "Roughness exponents to calculate multi-affine fractal exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 235(3), pages 327-333.
    6. Schumann, Aicko Y. & Kantelhardt, Jan W., 2011. "Multifractal moving average analysis and test of multifractal model with tuned correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2637-2654.
    7. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    8. Ayache, Antoine & Lévy Véhel, Jacques, 2004. "On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 119-156, May.
    9. Gao-Feng Gu & Wei-Xing Zhou, 2010. "Detrending moving average algorithm for multifractals," Papers 1005.0877, arXiv.org, revised Jun 2010.
    10. Zhao, Xiaojun & Shang, Pengjian & Lin, Aijing & Chen, Gang, 2011. "Multifractal Fourier detrended cross-correlation analysis of traffic signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3670-3678.
    11. Bashan, Amir & Bartsch, Ronny & Kantelhardt, Jan W. & Havlin, Shlomo, 2008. "Comparison of detrending methods for fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5080-5090.
    12. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
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    Cited by:

    1. Xiong, Gang & Yu, Wenxian & Xia, Wenxiang & Zhang, Shuning, 2016. "Multifractal signal reconstruction based on singularity power spectrum," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 25-32.
    2. Xi, Caiping & Zhang, Shunning & Xiong, Gang & Zhao, Huichang, 2016. "A comparative study of two-dimensional multifractal detrended fluctuation analysis and two-dimensional multifractal detrended moving average algorithm to estimate the multifractal spectrum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 454(C), pages 34-50.

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