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Singularity spectrum analysis of sea clutter is the key technology of detecting radar for sea target, which can discover the dynamic mechanism of the sea surface theoretically. In this paper, based on wavelet leaders the time-varying singularity spectrum distribution of sea clutters is proposed, which introduces time information to the traditional singularity spectrum, and displays the time-varying characteristic of singularity spectrum analytically. In theory, by way of self-windowed fractal signal, we introduce the time information to the traditional singularity spectrum, and realize multifractal spectrum distribution of sea clutters. In algorithm, based on the wavelet leaders, we adapt the process of embodying chirp-type and cusp-type singularities, and obtain the time-varying singularity spectrum distribution of sea clutters by the Legendre transform of the time-varying scaling function. In practice, we analyze the classical multifractal modelrandom wavelet series and the real sea clutter data of continuous wave Doppler radar in level III sea state. Experiments indicate that (1) the time-varying singularity spectrum distribution based on wavelet leaders can trace the time-varying scale characteristic and display the time-varying singularity spectrum distribution of sea clutters; (2) the algorithm possesses good statistical convergence, low computational cost, and passive moment property. The time-varying singularity spectrum distribution based on wavelet leaders may serve as a reference sample for nonlinear dynamics and multifractal signal processing.
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Keywords:
- wavelet leaders /
- multifractal formalism /
- time-singularity multifractal spectrum distribution /
- sea clutter
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[2] [3] [4] Mandelbrot B B 1986 Nonlinear Dynamics, Nijhof, Dordrecht p279
[5] [6] Grassberger P, Procaccia I 1983 Phys. Rev. Lett. 50 346
[7] Frisch U, Sulem P L 1984 Phys. Fluids 27 1921
[8] [9] Halsey T C, Jensen M H, Procaccia K P I 1986 Phys. Rev. A 33 1141
[10] [11] Kantelhardt J W, Zschiegner S A, Koscielny-Bunde E, Havlin S, Bunde A, Stanley H E 2002 Physica A 316 87
[12] [13] [14] Gu G F, Zhou W X 2006 Physical Rev. E 74 061104
[15] [16] Chhabra A, Jensen R 1989 Phys. Rev. Lett. 62 121327
[17] Gu G F, Zhou W X 2010 Phys. Rev. E. 82 011136
[18] [19] [20] Zhou W X 2008 Physical Rev. E 77 066211
[21] [22] Muzy J F, Bacry E, Arneodo A 1991 Phys. Rev. Lett. 67 3515
[23] [24] Bacry E, Arneodo A, Muzy J F 1993 J. Stat. Phys. 70 635
[25] Muzy J F, Bacry E, Arneodo A 1993 Phys. Rev. E 47 875
[26] [27] [28] Arneodo A, Argoul A, Muzy J F, Bacry E 1995 Fractals 1 629
[29] [30] Lashermes B, Jaffard S, Abry P 2005 ICASS, Philadelphia, USA 2005 pp161-164
[31] Xiong G, Yang X N, Zhao H C 2008 ICIC, Shanghai CCIS 15 pp541-548
[32] [33] [34] Arneodo A, Bacry E, Muzy J F. J 1998 Math. Phys. 39 4142
[35] [36] Aubry J M, Jaffard S 2002 Commun. Math. Phys. 227 483
[37] [38] Xiong G, Yang X N, Zhao H C 2005 IEEE MAPE, Beijing, 8 pp1236-1239
[39] [40] Liu N B, Guan J, Huang Y, Wang G Q, He Y 2012 Acta Phys. Sin. 61 190503 (in Chinese) [刘宁波, 关键, 黄勇, 王国庆, 何友 2012 61 190503]
[41] Xing H Y, Gong P, Xu W 2012 Acta Phys. Sin. 61 160504 (in Chinese) [行鸿彦, 龚平, 徐伟 2012 61 160504]
[42] [43] W He J B, Liu Z, Hu S L 2011 Acta Phys. Sin. 60 110208 (in Chinese) [贺静波, 刘忠, 胡生亮 2011 60 110208]
[44] [45] Yang J, Bian B M, Yan Z G, Wang C Y, Li Z H 2011 Acta Phys. Sin. 60 100506 (in Chinese) [杨娟, 卞保民, 闫振纲, 王春勇, 李振华 2011 60 100506]
[46] [47] Xiong G, Zhang S N, Liu Q 2012 Physica A 391 4727
[48] [49] p231 (in Chinese) [Falconer K 2007分形几何: 数学基础及其应用(第2版) (北京: 人民邮电出版社)第231页]
[50] Falconer K 2007 Fractal Geometry: Mathematical Foundations and Applications (2nd Ed.) (Beijing: Posts & Telecom Press)
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[1] Aanstassopoulos V, Lampropolous G A 1995 IRC, Washington, DC, p662
[2] [3] [4] Mandelbrot B B 1986 Nonlinear Dynamics, Nijhof, Dordrecht p279
[5] [6] Grassberger P, Procaccia I 1983 Phys. Rev. Lett. 50 346
[7] Frisch U, Sulem P L 1984 Phys. Fluids 27 1921
[8] [9] Halsey T C, Jensen M H, Procaccia K P I 1986 Phys. Rev. A 33 1141
[10] [11] Kantelhardt J W, Zschiegner S A, Koscielny-Bunde E, Havlin S, Bunde A, Stanley H E 2002 Physica A 316 87
[12] [13] [14] Gu G F, Zhou W X 2006 Physical Rev. E 74 061104
[15] [16] Chhabra A, Jensen R 1989 Phys. Rev. Lett. 62 121327
[17] Gu G F, Zhou W X 2010 Phys. Rev. E. 82 011136
[18] [19] [20] Zhou W X 2008 Physical Rev. E 77 066211
[21] [22] Muzy J F, Bacry E, Arneodo A 1991 Phys. Rev. Lett. 67 3515
[23] [24] Bacry E, Arneodo A, Muzy J F 1993 J. Stat. Phys. 70 635
[25] Muzy J F, Bacry E, Arneodo A 1993 Phys. Rev. E 47 875
[26] [27] [28] Arneodo A, Argoul A, Muzy J F, Bacry E 1995 Fractals 1 629
[29] [30] Lashermes B, Jaffard S, Abry P 2005 ICASS, Philadelphia, USA 2005 pp161-164
[31] Xiong G, Yang X N, Zhao H C 2008 ICIC, Shanghai CCIS 15 pp541-548
[32] [33] [34] Arneodo A, Bacry E, Muzy J F. J 1998 Math. Phys. 39 4142
[35] [36] Aubry J M, Jaffard S 2002 Commun. Math. Phys. 227 483
[37] [38] Xiong G, Yang X N, Zhao H C 2005 IEEE MAPE, Beijing, 8 pp1236-1239
[39] [40] Liu N B, Guan J, Huang Y, Wang G Q, He Y 2012 Acta Phys. Sin. 61 190503 (in Chinese) [刘宁波, 关键, 黄勇, 王国庆, 何友 2012 61 190503]
[41] Xing H Y, Gong P, Xu W 2012 Acta Phys. Sin. 61 160504 (in Chinese) [行鸿彦, 龚平, 徐伟 2012 61 160504]
[42] [43] W He J B, Liu Z, Hu S L 2011 Acta Phys. Sin. 60 110208 (in Chinese) [贺静波, 刘忠, 胡生亮 2011 60 110208]
[44] [45] Yang J, Bian B M, Yan Z G, Wang C Y, Li Z H 2011 Acta Phys. Sin. 60 100506 (in Chinese) [杨娟, 卞保民, 闫振纲, 王春勇, 李振华 2011 60 100506]
[46] [47] Xiong G, Zhang S N, Liu Q 2012 Physica A 391 4727
[48] [49] p231 (in Chinese) [Falconer K 2007分形几何: 数学基础及其应用(第2版) (北京: 人民邮电出版社)第231页]
[50] Falconer K 2007 Fractal Geometry: Mathematical Foundations and Applications (2nd Ed.) (Beijing: Posts & Telecom Press)
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