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Digital differentiators enable the computation of the derivative of a continuous-time signal at discrete time instances, and they are used in many signal processing applications. This paper derives a unified filter order estimate for digital differentiators that are realized with linear-phase finite-length impulse response filters and designed in the minimax sense. The estimate is useful at the high-level system design when assessing the implementation complexity and it enables fewer designs when finding the minimal filter order required to satisfy a prescribed tolerable approximation error. The proposed unified estimate covers both wideband and lowpass differentiators of integer degrees up to ten. Furthermore, degree-individual filter order estimates are derived which improve and extend previous results. The performance of both the unified and degree-individual order estimates is evaluated through simulation examples and compared with previous estimates. [ABSTRACT FROM AUTHOR]

Heart rate variability (HRV) analysis is considered as a preliminary diagnosis method to check the cardiac health of the human heart. The reliability of the HRV analysis system solely depends on the accuracy of the QRS complex detector. Hence, in this paper, an optimally designed digital differentiator (DD) for precise detection of QRS complex is proposed. The proposed DD is designed by using an efficient evolutionary optimization technique called gases Brownian motion optimization (GBMO) algorithm and is used in the preprocessing stage of the QRS detector. In GBMO algorithm, a balanced trade-off is maintained between both the exploration and the exploitation phases to find the global optimum solution. The electrocardiogram signal is preprocessed by using the proposed DD to generate the feature signals corresponding to the R-peaks only. The detection technique utilizes the principle of Hilbert transform and zeroes crossing detection. The proposed approach is verified against all the first channel records of MIT/BIH arrhythmia database by considering the standard QRS detection performance metrics and produces a sensitivity (Se) of 99.92%, positive predictivity (+P) of 99.92%, detection error rate (DER) of 0.1562%, QRS detection rate of 99.92%, accuracy (Acc) of 99.84%, and F score of 0.9992%. With respect to the standard performance metrics, the proposed QRS detector outperforms all the recently reported QRS detection techniques. [ABSTRACT FROM AUTHOR]