Optimal analog‐to‐digital transformation of fractional‐order Butterworth filter using binomial series expansion with Al‐Alaoui operator,International Journal of Circuit Theory and Applications

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Optimal analog‐to‐digital transformation of fractional‐order Butterworth filter using binomial series expansion with Al‐Alaoui operator
International Journal of Circuit Theory and Applications ( IF 1.8 ) Pub Date : 2020-11-26 , DOI: 10.1002/cta.2908
Shibendu Mahata ₁ , Rajib Kar ₁ , Durbadal Mandal ₁

Affiliation

This paper deals with the optimal analog‐to‐digital transformation of fractional‐order Butterworth filter (FOBF) in terms of infinite impulse response templates. The fractional‐order transfer function of the analog FOBF is transformed into its digital counterpart by employing the Binomial series expansion of different truncation orders, based on the Al‐Alaoui operator. This nonoptimal solution is then treated as an initial point for a local search optimizer such as the Nelder–Mead simplex (NMS) algorithm and also injected as a super‐fit individual in the initial population of a global search constrained evolutionary optimization algorithm (CEOA). Design stability and minimum‐phase response constraints are formulated for the super‐fit scheme. Both the techniques demonstrate good modeling performance; however, the super‐fit CEOA can markedly outperform the NMS method as the problem dimensionality increases.

中文翻译：

使用Al-Alaoui算子的二项式级数展开对分数阶Butterworth滤波器进行最佳模数转换

本文从无限脉冲响应模板的角度处理分数阶巴特沃斯滤波器（FOBF）的最佳模数转换。通过使用基于Al-Alaoui运算符的不同截断顺序的二项式级数展开，将模拟FOBF的分数阶传递函数转换为其数字对等函数。然后，此非最优解将被视为本地搜索优化器（例如Nelder–Mead单纯形法（NMS）算法）的起点，并作为超适合个体注入到全局搜索约束进化优化算法（CEOA）的初始种群中。为超级拟合方案制定了设计稳定性和最小相位响应约束。两种技术都表现出良好的建模性能。然而，

更新日期：2021-01-15

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