Cultural firework algorithm and its application for digital filters design

The substance of the digital filter design is a multi-parameter optimisation problem. This paper presents a joint objective function to design finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters, and a cultural firework (CF) algorithm is proposed to implement filter designs. The design of the filter is transformed into the constrained optimisation problem, and the cultural firework algorithm is used to search optimal value of filter design parameters in the parameter space with parallel search. The proposed cultural firework algorithm is a multi-dimensional search algorithm for optimisation of real numbers, which uses mechanisms of cultural evolution to update the locations of cultural sparks. Computer simulations have showed that FIR and IIR digital filters based on the CF algorithm are superior to previous filters based on particle swarm optimisation (PSO), quantum-behaved particle swarm optimisation (QPSO) and adaptive quantum-behaved particle swarm optimisation (AQPSO) in the convergence speed and optimisation results. The effectiveness and superiority of the CF are also demonstrated by computer simulations.