This paper approximates the behavior of low-pass Bessel filter in fractional domain using the Interior search algorithm (ISA). A detailed analysis has been done with sensitivity analysis, W-plane stability and absolute percentage error (gain and cut-off frequency) to study the low-pass fractional order filter. The work focuses on the analysis and design of fractional filter with two cases. In the first case, the design and simulation of [Formula: see text] order low-pass Bessel filter has been done using MATLAB for [Formula: see text] value ranging from 0.1 to 0.9. SPICE simulation of 1.2, 1.5 and 1.9 order low-pass Bessel filter using fractional order capacitor of order [Formula: see text] with Tow–Thomas biquad have been performed. In the second case, low-pass ([Formula: see text] order Bessel filter has been simulated and designed using MATLAB, where [Formula: see text] and [Formula: see text] are two fractional order elements of a different order. SPICE simulation for different values of [Formula: see text] and [Formula: see text] have been done using two fractional order capacitors of [Formula: see text] and [Formula: see text] order with Tow–Thomas biquad.

中文翻译：

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优化分数阶低通贝塞尔滤波器的分析与设计

本文使用内部搜索算法 (ISA) 逼近分数域中低通贝塞尔滤波器的行为。对灵敏度分析、W 平面稳定性和绝对百分比误差（增益和截止频率）进行了详细分析，以研究低通分数阶滤波器。工作重点是分式滤波器的分析与设计，分两种情况。在第一种情况下，[公式：见正文]阶低通贝塞尔滤波器的设计和仿真是使用MATLAB完成的，[公式：见正文]取值范围为0.1到0.9。已经使用带有 Tow-Thomas 双二阶的分数阶电容器 [公式：见正文] 对 1.2、1.5 和 1.9 阶低通贝塞尔滤波器进行了 SPICE 仿真。在第二种情况下，低通（[公式：见正文]阶贝塞尔滤波器已经使用MATLAB进行了仿真和设计，其中 [Formula: see text] 和 [Formula: see text] 是两个不同阶的分数阶元素。[Formula: see text] 和 [Formula: see text] 的不同值的 SPICE 仿真是使用两个分数阶电容器 [Formula: see text] 和 [Formula: see text] 阶和 Tow–Thomas biquad 完成的。