Efficient Design of Zero-Phase Riesz Fractional Order Digital Differentiator Using Manta-Ray Foraging Optimisation for Precise Electrocardiogram QRS Detection

Abstract

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.

Keywords

• ECG
• FIR filter
• fractional order Riesz digital differentiator
• Manta-Ray foraging optimisation
• zero-phase