Optimal design of wideband digital integrators and differentiators using harmony search algorithm

Abstract

This paper presents an efficient approach to design stable, wideband, and infinite impulse response digital integrators (DIs) and digital differentiators (DDs) of first, second, third, and fourth order using an evolutionary optimization algorithm called harmony search (HS). In recent years, although wideband DIs and DDs have been designed using metaheuristic optimization techniques such as simulated annealing, genetic algorithm, and particle swarm optimization (PSO), these algorithms lead to sub‐optimal solutions because of stagnation and premature convergence. HS algorithm, however, promises an enhanced frequency response for DIs and DDs because of the better exploration and exploitation of the search space. Simulation results demonstrate the superiority of HS‐based designs as compared with three well‐known benchmark evolutionary optimization algorithms, namely real coded genetic algorithm (RGA), PSO, and differential evolution (DE) based designs by yielding the least values of different magnitude response error metrics. Parametric and non‐parametric statistical hypothesis tests are also conducted to compare the consistency in the performance of HS‐based DIs and DDs with those of the designs based on RGA, PSO, and DE. The proposed HS‐based designs also outperform those of the designs based on both classical and evolutionary optimization approaches reported in recent literature in terms of the maximum absolute magnitude error metric.

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

“…From Table , it can be observed that RMSME value of −23.42 dB is obtained by Mahata et al, whereas, the proposed approach results in the lowest RMSME value of −24.95 dB. This ensures an improvement of 6.53% in the proposed SSA‐based DD over the DD reported in Mahata et al The percentage of improvement (PI) incurred by the proposed approach over all the reported state‐of‐the‐art DDs by considering the RMSME metrics is presented in Table .…”

“…The FIR filter‐based designs are inherently stable and provide linear phase characteristics . 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 .…”

“…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, . Also, for the DDs type search problem, where the nature of search landscape is discontinuous, multimodal, multidimensional, non‐uniform, and nonlinear, heuristic and metaheuristic type evolutionary optimization algorithms provide near‐optimal global solutions .…”

“…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, . Also, for the DDs type search problem, where the nature of search landscape is discontinuous, multimodal, multidimensional, non‐uniform, and nonlinear, heuristic and metaheuristic type evolutionary optimization algorithms provide near‐optimal global solutions . In this work, the IIR type first‐order DD is designed by using a recently published swarm intelligence technique‐based search method called SSA for accurately preprocessing the ECG signal.…”

Infinite Impulse Response Approximations to the Non-integer Order Integrator Using Cuckoo Search Algorithm

“…Literature survey reveals that metaheuristics have shown promising results in the field of digital filter design [16,17,18]. Hence, more research effort should be directed towards the design of NOIs based on the nature-inspired optimization algorithms.…”