This article introduces a new design of an optimised zero-phase response fractional order digital differentiator (FODD) called Riesz FODD of half order by employing a recently developed Manta-Ray Foraging Optimisation (MRFO) for improved and precise electrocardiogram QRS detection. A new weighted cost function is developed that precisely considers the characteristics of an ideal Riesz fractional-order differentiator. Simulation tests of the rational approximations of the Riesz FODD based on the MRFO algorithm ensure close correspondence with the theoretical zero-phase and near-ideal magnitude responses and sensibly supersede the Least-squares method, Convex optimisation, Flower Pollination Algorithm, and Artificial Bee Colony based Riesz FODD designs. The Zero-phase response of the proposed Riesz FODD assists in preserving the features of the differentiated ECG precisely at the same time instant where they occur in the unfiltered signal. Additionally, the optimal magnitude characteristics of the proposed Riesz FODD help to obtain highly accurate differentiated ECG. These two indigenous properties of the proposed Riesz FODD accommodate the QRS detector to precisely identify the R-peak location and thus sensibly escalate the QRS detection accuracy when tested against several real electrocardiogram (ECG) signals of the PhysioNet ECG repository.

中文翻译：

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利用Manta射线觅食优化实现零相Riesz分数阶数字微分器的高效设计，以实现精确的心电图QRS检测

本文通过采用最新开发的Manta-Ray觅食优化（MRFO）来改进和精确的心电图QRS检测，介绍了一种优化的零相位响应分数阶数字微分器（FODD）的新设计，称为半阶Riesz FODD。开发了一种新的加权成本函数，该函数精确地考虑了理想Riesz分数阶微分器的特性。基于MRFO算法的Riesz FODD有理逼近的仿真测试确保与理论上的零相位和接近理想的幅度响应紧密对应，并合理地取代了最小二乘方法，凸优化，花授粉算法和人工蜂群基于Riesz FODD的设计。提出的Riesz FODD的零相位响应有助于精确地保留微分ECG的特征，同时又出现在未经滤波的信号中。此外，建议的Riesz FODD的最佳幅度特性有助于获得高度精确的差异化ECG。拟议的Riesz FODD的这两个固有属性可容纳QRS检测器，以精确识别R峰位置，从而在针对PhysioNet ECG储存库的几个真实心电图（ECG）信号进行测试时，合理地提高QRS检测精度。