Wavelet transform modulus maxima based fractal correlation analysis

Abstract.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. [C. Meneveau, K.R. Sreenivasan, Phys. Rev. A 41, 894 (1990)] 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.