title: Extraction of backgrounds in fluctuating systems.
abstract: We undertake an extensive analytical study on the "generalized detrended fluctuation analysis" method, designed to detect the scaling behaviors of fluctuating systems but exclude out the influences of the backgrounds (or the trends). Through our extensive studies, we systematically extract out the exact backgrounds (or the trends) of the fluctuating systems to any order, expressed in terms of the Legendre polynomial. Our results are exact and can be applied to any (1+1)-dimensional continuous fluctuating systems.
authors.affiliation: Department of Physics, National Taiwan University, Taipei, Taiwan, Republic of China.
authors.forename: Ning-Ning
authors.initials: NN
authors.lastname: Pang
authors.forename: Wen-Jer
authors.initials: WJ
authors.lastname: Tzeng