Optimal SSA‐based wideband digital differentiator design for cardiac QRS complex detection application

Abstract

In this paper, a computationally efficient, highly accurate, wideband, stable, and minimum phase infinite impulse response type first-order digital differentiator (DD) is designed by employing a swarm intelligence-based search method called Salp Swarm Algorithm (SSA) for the QRS complex detection application. The optimal coefficients of the DD are computed by minimizing a suitable fitness function to meet the ideal differentiator magnitude response characteristics.The simulation results and the root mean square magnitude error metric justify the superiority of the proposed SSA-based DD design as compared with all other differentiators employed in the QRS complex detection application, and the reported first-order DDs based on the numerical methods and the other evolutionary algorithms. The electrocardiogram signal is preprocessed by the proposed DD to generate the feature signal corresponding to each QRS complex.The generated feature signal is used as a marker to identify the exact occurrence of the QRS complex by using an adaptive threshold-based detection logic. The proposed DD-based QRS detection approach achieves a sensitivity (Se), positive prediction (PP), detection error rate (DER), and accuracy (Acc) of 99.94%, 99.93%, 0.1279%, and 99.87%, respectively, when validated against MIT/BIH arrhythmia database. Also, against the QT database, the proposed QRS detector produces a Se of 99.93%, PP of 99.97%, DER of 0.09%, and Acc of 99.90%. The performance of the proposed QRS detection technique is compared with the methods already reported in the recent literature, and the superiority of the proposed approach is established with respect to different standard performance metrics. The noise tolerance capability of the proposed QRS detector is demonstrated against MIT/BIH noise stress test database. KEYWORDS digital differentiator (DD), electrocardiogram (ECG), QRS complex detection, Salp swarm algorithm (SSA) /journal/jnm 1 of 25sinus rhythm. Any deviation from the standard sinus rhythm, called arrhythmia, can be detected by close observation of the shape and the interval duration of the waves. Hence, from a diagnosis point of view, the calculation of the wave interval is essential and can be determined by accurately identifying the time of occurrence of the R-wave/R-peak (peak of the QRS wave). From the appearance of the R-wave, the R-R interval duration can be estimated. Also, by knowing the occurrence of the R-waves, several post-processing applications like heartbeat classification, foetal heart rate monitoring, ECG coder, and heart rate variability analysis can be implemented. The time of occurrences of the R-waves is considered as markers to identify the time of the presence of the P/T-waves, QRS interval, PR interval, QT interval, ST segment, and PQ segment. 1 This information plays a pivotal role to diagnose various cardiac diseases. With the accurate estimation of the QT interval and the heart rate, a potentially dangerous disease called hypoglycaemia (low blood glucose level) can be monitored noninvasively...

Design and Optimization of Enhanced Magnitude and Phase Response IIR Full-Band Digital Differentiator and Integrator Using the Cuckoo Search Algorithm

“…To validate the proposed approach, we compare the performance of the designed DDs and DIs with designs of DDs and DIs in the published literature using other techniques and algorithms. Specifically, we compared with SA (simulated annealing) [18], GA (genetic algorithm) [18], FP (Fletcher and Powell) [18], PSO (particle swarm optimization) [19], HS (harmony search) [21], BA (bat algorithm) [22], HFPA (hybrid flower pollination algorithm) [23] and SSA (salp swarm algorithm) [26]. The comparison is made based on the magnitude response and the phase response of the designed DDs and DIs.…”

“…Figures 4 through 6 show the AME comparison. As can be seen, the second order designed IIR DD based on the proposed approach has less AME than that of DDs designed using GA [18], PSO [19], HS [21], BA [22], HFPA [23] and approximately similar AME to that of DDs designed using the SA [18], FP [18] and SSA [26]. For the third order, the designed IIR DD based on the proposed approach has less AME than that of DDs designed using the SA [18], FP [18], GA [18], HS [21], and HFPA [23] but similar AME to that of DD designed using the SSA [26].…”

“…As can be seen, the second order designed IIR DD based on the proposed approach has less AME than that of DDs designed using GA [18], PSO [19], HS [21], BA [22], HFPA [23] and approximately similar AME to that of DDs designed using the SA [18], FP [18] and SSA [26]. For the third order, the designed IIR DD based on the proposed approach has less AME than that of DDs designed using the SA [18], FP [18], GA [18], HS [21], and HFPA [23] but similar AME to that of DD designed using the SSA [26]. And finally, the fourth order IIR DD designed based on the proposed approach has less AME than that of the DDs designed using the SA [18], GA [18], FP [18], PSO [19], HS [21], BA [22], HFPA [23] and similar AME to that of the DD designed using the SSA [26].…”

“…Many analytical approaches to design DD and DI with some desired characteristics have been proposed and demonstrated in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The use of evolutionary and swarm intelligence algorithms to design and optimize the performance of DDs and DIs has been reported in [17][18][19][20][21][22][23][24][25][26]. For examples, the design of DD and DI is demonstrated using genetic algorithm (GA) in [17], simulated annealing (SA), GA, and modified Fletcher and Powell (FP) optimization in [18], particle swarm optimization (PSO) in [19].…”

“…Design of FIR DD based on the L1 optimality criterion using the BA and the PSO is demonstrated in [24]. Wideband IIR DD and DI are designed using the salp swarm algorithm (SSA) in [25][26]. In addition, the design of low pass DD has been considered in [27][28][29][30][31][32][33][34][35][36][37].…”