(N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response
(N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response
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用于逼近巴特沃斯响应的非级联实现的 (N + α) 阶低通和高通滤波器传递函数
DOI：
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发表时间：
2021
影响因子：
3
通讯作者：
D. Andriukaitis
中科院分区：
文献类型：
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作者：
D. Kubánek;J. Koton;J. Jerabek;D. Andriukaitis
给出了采用非级联多反馈模拟结构实现的分数阶全极点低通频率滤波器传递函数(N+α)的公式。目的是根据滤波器阶数和传递函数中分数阶项的分布来确定该传递函数的系数及其可能的变体。使用优化算法来逼近目标巴特沃斯低通幅度响应，同时评估逼近误差。提供了用于计算传递函数系数的插值方程。还给出了分数阶低通滤波器到高通滤波器的变换的示例。通过带有运算跨导放大器和分数阶元件的多反馈滤波器的仿真验证了结果。
The formula of the all-pole low-pass frequency filter transfer function of the fractional order ( N + α ) designated for implementation by non-cascade multiple-feedback analogue structures is presented. The aim is to determine the coefficients of this transfer function and its possible variants depending on the filter order and the distribution of the fractional-order terms in the transfer function. Optimization algorithm is used to approximate the target Butterworth low-pass magnitude response, whereas the approximation errors are evaluated. The interpolated equations for computing the transfer function coefficients are provided. An example of the transformation of the fractional-order low-pass to the high-pass filter is also presented. The results are verified by simulation of multiple-feedback filter with operational transconductance amplifiers and fractional-order element.