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The Short-Time Multifractal Formalism: Definition and Implement

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Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques (ICIC 2008)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 15))

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Abstract

Although multifractal descirbles the singularity distribution of SE, there is no time information in the multifractal formalism, and the time-varying singularity distribution indicates the spatial dynamics character of system. Therefore, the definition and implement of the short-time multifractal formalism is proposed, which is the prelude of time time-singularity spectra distribution. In this paper, the singularity analysis of windowed signal was given, further the short-time hausdorff spectum was deduced. The Partition Function and Short-time Legendre Spectrum was fractal statistical distribution of SE. WTMM method is popular in implement of MFA, and in section IV,Short-time multifractal spectra based on WTMM is brough forward.

This paper is supported by Post-doctoral Research Foundation of Province Zhejiang (No. 2006-bsh-27) and National Science foundation Research: Time-Dimension Spectral Distribution and the Affine Class Time-Frequency Processing of Stochastic Multifratal (No. 60702016).

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Authors and Affiliations

  1. NO.36 Research Institute of CETC, National Laboratory of Information Control Technology For Communication System, Jiaxing, Zhe-Jiang, 314001, China

    Xiong Gang & Yang Xiaoniu

  2. Electronic engineering dept., NJUST, Nanjing, 210094, China

    Xiong Gang & Zhao Huichang

Authors
  1. Xiong Gang
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  2. Yang Xiaoniu
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  3. Zhao Huichang
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Editor information

De-Shuang Huang Donald C. Wunsch II Daniel S. Levine Kang-Hyun Jo

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Gang, X., Xiaoniu, Y., Huichang, Z. (2008). The Short-Time Multifractal Formalism: Definition and Implement. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. ICIC 2008. Communications in Computer and Information Science, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85930-7_69

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  • DOI: https://doi.org/10.1007/978-3-540-85930-7_69

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85929-1

  • Online ISBN: 978-3-540-85930-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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