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Wavelet leaders-based multifractal spectrum distribution

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Abstract

We introduce a new time-singularity multifractal spectrum distribution (TS-MFSD) approach based on wavelet leaders (WL) and study its properties. Compared against the previous TS-MFSD based on the wavelet coefficient and the wavelet transform module maxima method, we show first that WL-based formalism can obtain the time-singularity multifractal distribution over its entire time-singularity plane, second that it holds when applied to process embodying chirp-type or oscillating singularities (as opposed to cusp-type ones), and third that it has less computational cost benefitting from the fast decomposition algorithms and can be used for signals of arbitrary length. We illustrate these results on the multifractal stochastic processes and real sea clutter data, which show that WL-based MFSD has excellent theoretical and practical performance.

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Acknowledgments

The authors would be grateful to the anonymous reviewers for helpful comments and valuable suggestions that led to a significant improvement of the manuscript. This work was supported by the National Natural Science Foundation of China (NSFC, Grant Number 61171168, 61301216, & 60702016).

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Authors and Affiliations

  1. Institute of Photoelectric Information, University of Shanghai for S&T, Shanghai, 200093, People’s Republic of China

    Gang Xiong

  2. School of Electronic and Optical Engineering, Nanjing University of S&T, Nanjing, 210094, People’s Republic of China

    Gang Xiong, Shuning Zhang, Huichang Zhao & Caiping Xi

  3. School of Optical Electrical and Computer Engineering, University of Shanghai for S&T, Shanghai, 200093, People’s Republic of China

    Gang Xiong

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  1. Gang Xiong
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  2. Shuning Zhang
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  3. Huichang Zhao
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  4. Caiping Xi
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Correspondence to Gang Xiong or Shuning Zhang.

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Xiong, G., Zhang, S., Zhao, H. et al. Wavelet leaders-based multifractal spectrum distribution. Nonlinear Dyn 76, 1225–1235 (2014). https://doi.org/10.1007/s11071-013-1206-z

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