Optimal design of 2-D FIR digital differentiator using $$L_1$$L1-norm based cuckoo-search algorithm

In this article, an optimal design of two-dimensional finite impulse response digital differentiators (2-D FIR-DD) with quadrantally odd symmetric impulse response is presented. The design problem of 2-D FIR-DD is formulated as an optimization problem based on the $$L_1$$L1-error fitness function. The novel error fitness function is based on the $$L_1$$L1 norm which is unique and is liable to produce a flat response. This design methodology incorporates advantages of $$L_1$$L1-error approximating function and cuckoo-search algorithm (CSA) which is capable of attaining a global optimal solution. The optimized system coefficients are computed using $$L_1$$L1-CSA and performance is measured in terms of magnitude response, phase response, absolute magnitude error and elapsed time. Simulation results have been compared with other optimization algorithms such as real-coded genetic algorithm and particle swarm optimization and it is observed that $$L_1$$L1-CSA delivers optimal results for 2-D FIR-DD design problem. Further, performance of the $$L_1$$L1-CSA based 2-D FIR-DD design is evaluated in terms of absolute magnitude error and algorithm execution time to demonstrate their effect with variation in the control parameters of CSA.