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Physical Review E
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 trends͒. Through our extensive studies, we systematically extract out the exact backgrounds ͑or the trends͒ of the fluctuating systems to any order, expressed in terms of the Legendre polynomial. Our results are exact and can be applied to any (1ϩ1)-dimensional continuous fluctuating systems.doi:10.1103/physreve.69.031108 pmid:15089266 fatcat:bmo2z2dyf5aprbzsohupcqcrfu