Digital Multiple Notch Filter Design with Nelder-Mead Simplex Method

Abstract

Multiple notch filters are used to suppress narrow-band or sinusoidal interferences in digital signals. In this paper, we propose a novel optimization design technique of an infinite impulse response (IIR) multiple notch filter. It is based on the Nelder-Mead simplex method. Firstly, the system function of the desired notch filter is constructed to form the objective function of the optimization technique. Secondly, the design parameters of the desired notch filter are optimized by Nelder-Mead simplex method. A weight function is also introduced to improve amplitude response of the notch filter. Thirdly, the convergence and amplitude response of the proposed technique are compared with other Nelder-Mead based design methods and the cascade-based design method. Finally, the practicability of the proposed notch filter design technique is demonstrated by some practical applications.