Digital Differentiator Design Using L1-Norm and LS with GOA Algorithm

This paper proposed the design of advanced second and third-order Infinite Impulse Response (IIR) digital differentiators optimized using the Grasshopper Optimization Algorithm (GOA). The focus is on minimizing errors by applying L1-norm and Least Square (LS) fitness functions, leading to highly precise differentiators. The performance of the designed differentiators is benchmarked against established methods by calculating Maximum Normalized Magnitude Error (MNME) and Absolute Magnitude Error (AME). Extensive simulations in MATLAB demonstrate the superior performance of the proposed differentiators, achieving MNME values of −72.7052 dB for the second-order and −75.7473 dB for the third-order differentiators, significantly outperforming other techniques.