IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory

Romero, Miguel; Madrid, A.P. de; Mañoso, C.; Vinagre, Blas M.

doi:10.1016/j.isatra.2013.02.002

Cited by 45 publications

(23 citation statements)

References 22 publications

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“…For designing digital FOIs, two most widely used methods are direct and indirect discretization [3]. Based on these traditional methods, many research articles exist on the design of fractional-order infinite impulse response (IIR) integrators for digital signal processing applications [4][5][6][7]. In recent years, various nature inspired optimization algorithms like particle swarm optimization (PSO) [8], colliding bodies optimization [9], cuckoo search algorithm (CSA) [10] etc., had been studied extensively to obtain the optimal designs of FOIs.…”

Section: Introductionmentioning

confidence: 99%

Design and Implementation of Fractional-Order Microwave Integrator

Gupta¹,

Upadhyay²

2019

RADIOENGINEERING

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A novel design of fractional-order microwave integrator using shunt connected open-stubs with transmission line sections in cascade is proposed. Design is obtained by optimizing the L 1-norm based error function in Z-domain having not more than absolute magnitude error value of 0.01. Optimization is done using nature inspired cuckoo search algorithm. Superiority of the design in terms of magnitude error performance is identified by comparing it with the results obtained from some widely used benchmark optimization algorithms. The obtained design is implemented on a RT/Duroid 5880 substrate having 20 mil thickness, and results for the measured magnitude response are found to be in good agreement with ideal one over the frequency range of 1.0 GHz to 6.8 GHz.

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Section: Introductionmentioning

confidence: 99%

Design and Implementation of Fractional-Order Microwave Integrator

Gupta¹,

Upadhyay²

2019

RADIOENGINEERING

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“…However, to meet the same magnitude response characteristic, the FIR filter‐based approach needs higher filter order than IIR‐based approach . Several numerical methods‐based digital integrators (DIs) and DDs are reported in the literature . However, in the recent trend, the availability of the highly efficient evolutionary algorithms facilitates the researchers to solve the DD‐type optimization problems more efficiently without using S to Z transformation, .…”

Section: Introductionmentioning

confidence: 99%

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

Nayak

Saha

Kar

et al. 2018

Int J Numerical Modelling

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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...

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“…It may be noted that while variable DFOIs are reported in [25], however, this work deals with the accurate realization of fixed DFOIs using a bio-inspired optimization algorithm called CSO [26]. While all the DFOI design techniques cited in [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] employ a discretization operator, the approach presented in this paper can generate the optimal IIR filter coefficients for the DFOIs without using any such operator. Hence, the novelty of this paper is to present a single-step approach to obtain optimal and highly accurate DFOI models as compared with the multistep DFOI realization methods reported in [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Improved IIR-type fractional order digital integrators using cat swarm optimization

Mahata¹,

Saha²,

Kar³

et al. 2018

Turk J Elec Eng & Comp Sci

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Design of wideband infinite impulse response (IIR) digital fractional order integrators (DFOIs) based on a bio-inspired metaheuristic optimization approach called the cat swarm optimization (CSO) algorithm is presented in this paper. To investigate the efficiency of the proposed approach, the CSO-based DFOIs are evaluated against those of the approximations designed using real-coded genetic algorithm (RGA), standard particle swarm optimization (PSO),

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IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory

Cited by 45 publications

References 22 publications

Design and Implementation of Fractional-Order Microwave Integrator

Design and Implementation of Fractional-Order Microwave Integrator

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

Improved IIR-type fractional order digital integrators using cat swarm optimization

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