An Improved Design Technique of Digital Finite Impulse Response Filter for Notch Filtering

In this paper, an improved method for the design of finite impulse response (FIR) filter for notch filtering is devised using fractional derivative (FD). Optimal design of FIR notch filter is formed as minimization of mean squared error with respect to filter coefficients, subjected to fractional constraint imposed at notch frequency. Solution of this problem is computed using the Lagrange multiplier method. On experimental analysis, it is observed that the fidelity parameters like passband error (Er_p), notch bandwidth (BW_N), and maximum ripple (δ_p) varies nonlinearly with respect to FD values. Also, the exploration of suitable FD value is computationally costly. Thus, to acquire the best solution, modern heuristic methods known as hybrid particle swarm optimization (Hybrid-PSO), which is stimulated by the intelligence of some biological species, is employed. An exhaustive analysis results reveals that second-order FDCs approach results in drop of Er_p by 50%, and BW_N is improved by more 12%, while it is increased for only certain cases. It is also observed that the proposed methodology for convergence requires 100 iterations at most. The designed notch filter is tested for elimination of power line interference introduced in an electrocardiography (ECG) signal and efficient response is observed.