Optimal designing and realisation of two-dimensional FIR fractional order digital differentiator using colony predation algorithm

Conventional design techniques are inadmissible to design 2-D fractional order digital differentiators because the design problem is in multi-dimension which requires optimisation of a massive number of differentiator coefficients and execution time. Metaheuristic algorithms have the perspective of handling such complex problems. This work presents a methodology for 2-D FIR-FODD (finite impulse response-fractional order digital differentiator) with a colony predation algorithm (CPA) to solve the impulse response and achieve the desired fractional-order differentiator, with comparisons to existing algorithms based on control parameters, absolute magnitude error and execution time. The design demonstrates a close approximation, exhibiting an absolute magnitude error of 0.2675 for coefficient matrix of 15 × 15, surpassing current techniques in terms of performance. Specifically, the CPA method improves the absolute error and algorithm execution time by 73.37%, 201%, 57.32%, 45.95%©and 10.88%, compared to L1- RCGA, L1-PSO, L1-CSA, L1-VSO and DCT-III, respectively. The results confirm that the CPA-based technique is highly effective and reliable method for constructing the 2-D FIR-FODD. Additionally, the transfer function’s coefficients are analysed using direct form architecture in a Simulink model, and hardware utilisation is assessed by providing insights into hardware requirements.