Multi-Objective Big Bang–Big Crunch Optimization Algorithm For Recursive Digital Filter Design

The paper represents the design of recursive second order Butterworth low pass digital filter which optimizes both the magnitude and group delay simultaneously under the Multi-Objective Big Bang-Big Crunch Optimization algorithm. Multi-Objective problem of magnitude and group delay are solved using Multi-Objective BB-BC Optimization algorithm that operates on a complex, continuous search space and optimized by statistically determining the abilities of Big Bang Phase and Big Crunch Phase. Here both experimented fitness functions (magnitude error function and group delay error function) based on the mean squared error between the actual and the ideal filter response. MATLAB programming is used for implementation of proposed algorithm. Experimental results show that the proposed method can effectively optimize the magnitude and group delay functions simultaneously and by using this optimization algorithm, group delay becomes more constant in the passband than the other optimization algorithms. The Multi-Objective BB-BC Optimization seems to be promising tool for both IIR and FIR filter design especially in a dynamic environment where filter coefficients have to be adapted and fast convergence is of importance.