A complex adaptive Harmonic IIR notch filter

Abstract

A complex adaptive Harmonic IIR notch filter is proposed for estimating and tracking the frequency of periodic complex signals in a noisy harmonic environment. The transfer function of the developed notch filter consists of cascaded first-order complex transfer functions whose notch frequencies are constrained to the fundamental and harmonic frequencies. The least mean squares (LMS) algorithm is developed and a formula to determine the stability bound for the algorithm is derived. In addition, an improved simple scheme is devised to prevent the adaptive algorithm from converging to its local minima of the mean square error (MSE) function when the tracked signal fundamental frequency changes. Computer simulations validate the performance of the developed algorithm.