The Legendre Multifractal Spectrum Distribution Based on WTMM

In this paper, the time-varying Legendre multifractal spectrum is proposed. Similar to the Wigner-Ville time-frequency analysis, the time-delayed conjugation of analyzed signal is selected as the windows function, and the quadratic time-singularity exponent distribution of the instantaneous self-correlation is deduced based on the short-time multifractal analysis, i.e. quadratic time-singularity multifractal distribution. As a special form of Legendre spectrum, the Wavelet Transform Module Maxima (WTMM)Method of the quadratic time-singularity multifractal spectrum distribution is brought forward, and simulation based on WTMM proves the validity.