Abstract— In this paper, the design and optimization of infinite impulse response full-band digital differentiator (DD) using evolutionary and swarm intelligence algorithms is investigated. Different objective functions based on the absolute error, the squared absolute error and the min-max optimality criterion are investigated. The optimal DD parameters that result in the best minimum value of the investigated objective functions are obtained using differential evolution, particle swarm optimization, genetic algorithm and cuckoo search optimization methods. These algorithms are used due to their simplicity, efficiency and robustness in solving general multidimensional optimization problems. The investigation outcomes show that minimizing the absolute error gives the most flat magnitude response, and minimizing the squared absolute error gives almost the lowest mean error of the designed DD. In addition, a new objective function is proposed to improve the linearity of the phase response of the designed infinite impulse response full-band DD. It is found that the design of the DD using the differential evolution outperforms or at least is comparable to similar designs reported in the literature using other optimization methods.