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In this paper, wavelet transform was firstly used to analyze the singularity of a given signal, and then with the method of Wavelet Transform Modulus Maximum (WTMM), the characters of fractal set of triadic Cantor was studied. The results show that one can, not only determine the position of singular of signal, but also estimate the Hlder exponent h which describes the strength of singularity and other parameters, such as D(h) and τ(q) correctly. Finally, after applying this method to process temperature data in the Rayleigh-Bénard convection further, we found that the multifractal hierarchical and multi-scale structure underlying this flow could be entirely revealed from the parameters h, D(h) and τ(q), and the obtained results agree well with the ones determined from the viewpoint of fractal measures.
In this paper, wavelet transform was first used to analyze the singularity of a given signal, and then with the method of Wavelet Transform Modulus Maximum (WTMM), the characters of fractal set of triadic Cantor was studied. The results show that one can, not only determine the position of singular of signal, but also estimate of Hlder exponent h which describes the strength of singularity and other parameters, such as D (h) and τ (q) correctly. Finally, after applying this method to process temperature data in the Rayleigh-Bénard convection further, we found that the multifractal hierarchical and multi-scale structure underlying this flow could be entirely revealed from the parameters h, D (h) and τ (q), and the obtained results agree well with the ones determined from the viewpoint of fractal measures.