Optimal Design of Type 3 and Type 4 Linear Phase FIR Differentiators using the Genetic Algorithm

Abstract

In this article, the Genetic Algorithm (GA) approach inspired by the Darwin’s theory, “Survival of the fittest”, is used as a function in MATLAB for the optimal design of TYPE-3 and TYPE-4 linear phase FIR digital differentiators where the order of the desired differentiator is provided by the user. The optimal differentiator coefficients are obtained by minimizing the Least Mean Squared (LMS) error. In order to validate the proposed approach, extensive simulations are carried out for each type of differentiator. The simulation results confirmed that the GA outperforms the conventional method Parks-McClellan (PM) and the swam meta-heuristic Artificial Bee Colony (ABC).