A new design method for FIR notch filter using Fractional Derivative and swarm intelligence

Abstract

In this paper, a new design method for the finite impulse response (FIR) notch filters using fractional derivative (FD) and swarm intelligence technique is presented. The design problem is constructed as a minimization of the magnitude response error w.r.t. filter coefficients. To acquire high accuracy of notch filter, fractional derivative (FD) is evaluated, and the required solution is computed using the Lagrange multiplier method. The fidelity parameters like passband error, notch bandwidth, and maximum passband ripple vary non-linearly with respect to FD values. Moreover, the tuning of appropriate FD value is computationally expensive. Therefore, modern heuristic methods, known as the constraint factor particle swarm optimization (CFI-PSO), which is inspired by swarm intelligence, is exploited to search the best values of FDs and number of FD required for the optimal solution. After an exhaustive analysis, it is affirmed that the use of two FDs results in 21% reduction in passband error, while notch bandwidth is slightly increased by 2% only. Also, it has been observed that, in the proposed methodology, at the most 66 iterations are required for convergence to optimum solution. To examine the performance of designed notch filter using the proposed method, it has been applied for removal of power line interference from an electrocardiography (ECG) signal, and the improvement in performance is affirmed.