Wavelet Transform Modulus Maxima Based Fractal Correlation Analysis
D. C. Lin, Asif Hasan Sharif · 2008
The wavelet transform modulus maxima (WTMM) used in the singularity analysis of one fractal function is extended to study the fractal correlation of two multifractal functions. The technique is developed in the framework of joint partition function analysis (JPFA) proposed by Meneveau et al. [1] and is shown to be equally effective. In addition, we show that another leading approach developed for the same purpose, namely, relative multifractal analysis, can be considered as a special case of JPFA at a particular parameter setting. 1 Introdcution Fluctuations in many natural and artificial phenomena are found to exhibit fractal characteristics. In applications, this has been characterized by the so-called singularity spectrum of some numerical or experimental data. To understand the dynamics underlying the fractal, it is not uncommon that multiple data capturing different aspects of the phenomenon of interest are used in the analysis. For example, velocity and temperature flucutations are used to analyze the momentum and energy aspects of the multifractal hydrodynamic turbulence