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

Design of full-band infinite impulse response (IIR) digital differentiator (DD) and digital integrator (DI) based on the Lk-norm and the min-max optimality criteria have been demonstrated in literature. However, the designed IIR DDs and DIs using these criteria do not have linear phase or have unsatisfactory magnitude response. In this paper, a novel approach to design, optimize and improve the magnitude response and the linearity of the phase response of IIR DD and DI using the cuckoo search (CS) optimization algorithm is proposed. The proposed approach is based on a varied Lk-norm where $k$ linearly increases with the number of the frequency samples between the values 1 and 2. The design and optimization of DDs and DIs are carried out using the CS optimization method due to its simplicity, efficiency, and robustness in solving general multidimensional optimization problems. The performance of the designed DDs and DIs using the proposed approach is compared with designs based on different criteria and algorithms available in literature. The comparison shows that the designed DDs and DIs based on the proposed approach have better phase responses and better or at least comparable magnitude responses compared to those of DDs and DIs designed using other methods in the literature.