The Short-Time Multifractal Formalism: Definition and Implement
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.
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