In this paper we propose a modification to a second order approximation of the fractional-order Laplacian operator, sα, where 0 < α < 1. We show how this proposed modification can be used to change the ripple error of both the magnitude and phase responses of the approximation when compared to the ideal case. Equal-ripple magnitude and phase responses that have both less cumulative error and less maximum ripple deviation are presented using this modification. A 1st order lowpass filter with fractional step of 0.8, that is of order 1.8, is implemented using the proposed approximation. Experimental results verify the operation of this approximation in the realization of the fractional step filter.
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机译:在本文中,我们提出了对分数阶拉普拉斯算子s α sup>的二阶近似的修正,其中0 <α<1。与理想情况相比,近似值的幅度和相位响应的误差。使用此修改,可以同时具有较小的累积误差和较小的最大纹波偏差的等波纹幅度和相位响应。使用提出的近似值实现了分数阶跃为0.8的1 st sup>低通滤波器。实验结果证明了这种近似在分数阶阶滤波器实现中的作用。
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