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Traditional methods for nonlinear dy-namic analysis,such as correlation dimension,Lyapunov exponent,approximate entropy,detrended fluctuation analysis,using a single parameter,cannot fully describe the extremely sophisticated behavior of electroencephalogram (EEG). The multifractal for-malism reveals more “hidden” information of EEG by using singularity spectrum to characterize its nonlin-ear dynamics. In this paper,the zero-crossing time intervals of sleep EEG were studied using multifractal analysis. A new multifractal measure Δasα was pro-posed to describe the asymmetry of singularity spec-trum,and compared with the singularity strength range Δα that was normally used as a degree indi-cator of multifractality. One-way analysis of variance and multiple comparison tests showed that the new measure we proposed gave better discrimination of sleep stages,especially in the discrimination be-tween sleep and awake,and between sleep stages 3 and 4.
Traditional methods for nonlinear dy-namic analysis, such as correlation dimension, Lyapunov exponent, approximate entropy, detrended fluctuation analysis, using a single parameter, can not fully describe the extremely sophisticated behavior of electroencephalogram (EEG). The multifractal for-malism reveals more “ hidden ”information of EEG by using singularity spectrum to characterize its nonlin-ear dynamics. In this paper, the zero-crossing time intervals of sleep EEG were studied using multifractal analysis. A new multifractal measure Δasα was pro-posed to describe the asymmetry of singularity spec-trum, and compared with the singularity strength range Δα that was normally used as a degree indi-cator of multifractality. One-way analysis of variance and multiple comparison tests showed that the new measure we proposed gave better discrimination of sleep stages, especially in the discrimination be-tween sleep and awake, and between sleep stages 3 and 4.