Multifractal signal reconstruction based on singularity power spectrum. (October 2016)

• Record Type: Journal Article
• Authors: Xiong, Gang; Yu, Wenxian; Xia, Wenxiang; Zhang, Shuning
• Is Part Of: Chaos, solitons and fractals. Volume 91(2016)
• Page Start: 25
• Page End: 32
• Publication Date: 2016-10
• Subjects: Multifractal reconstruction -- Singularity exponent -- Singularity power spectrum -- Multifractal spectrum; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2016.04.021
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: We propose a novel multifractal reconstruction method based on singularity power spectrum analysis (MFR-SPS). The proposed MFR-SPS method has better power characteristic than the algorithm in Fraclab. Further, the SPS-ISE algorithm performs better than the SPS-MFS algorithm. Based on the proposed MFR-SPS method, we can restructure singularity white fractal noise (SWFN) and linear singularity modulation (LSM) multifractal signal, in equivalent sense, similar with the linear frequency modulation(LFM) signal and WGN in the Fourier domain. Abstract: Fractal reconstruction (FR) and multifractal reconstruction (MFR) can be considered as the inverse problem of singularity spectrum analysis, and it is challenging to reconstruct fractal signal in accord with multifractal spectrum (MFS). Due to the multiple solutions of fractal reconstruction, the traditional methods of FR/MFR, such as FBM based method, wavelet based method, random wavelet series, fail to reconstruct fractal signal deterministically, and besides, those methods neglect the power spectral distribution in the singular domain. In this paper, we propose a novel MFR method based singularity power spectrum (SPS). Supposing the consistent uniform covering of multifractal measurement, we control the traditional power law of each scale of wavelet coefficients based on the instantaneous singularity exponents (ISE) or MFS, simultaneously control the singularity power law based on the SPS, and deduce the principle and algorithm of MFR based on SPS. Reconstruction simulation and error analysis of estimated ISE, MFS and SPS show the effectiveness and the improvement of the proposed methods compared to those obtained by the Fraclab package.