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根据特定峰信号微分的极值和过零点随着微分阶次的变化而改变,建立了峰信号的极值和过零点与其相应微分阶次的关系式,进而得到了两类参数估计器,利用这些估计器可以估计出Gaussian峰、Lorentzian峰和Tsallis峰信号的特征参数.首先,利用分数阶微分器获得特定峰信号的分数阶微分;其次,根据峰信号的极值与其微分阶次的关系式和过零点与其微分阶次的关系式,建立了估计器Ⅰ和估计器Ⅱ;再利用这些估计器便可以提取峰信号的特征参数;最后,用Tsallis峰作为子峰模型对未知重叠峰信号进行分辨.仿真和实测重叠峰信号的分辨实验表明本方法简单高效.
According to the change of the extremum and zero-crossing of the differential of certain peak signal with the change of differential order, the relationship between the extremum of the peak signal and the corresponding derivative order of the zero-crossing point is established. Then two kinds of parameter estimators are obtained, These estimators can estimate the characteristic parameters of Gaussian peak, Lorentzian peak and Tsallis peak signal.First, the fractional differential of specific peak signal is obtained by fractional-order differentiator. Secondly, according to the relation between the extremum of peak signal and its differential order And the relationship between the zero-crossing point and its differential order, the estimator I and the estimator II are established. Then, the characteristic parameters of the peak signal can be extracted by using these estimators. Finally, the Tsallis peak is used as the sub-peak model for the unknown overlapping peak signal Resolution.The experimental results show that the proposed method is simple and efficient.