Novel adaptive IIR filter for frequency estimation and tracking [DSP Tips&Tricks]

In many applications, a sinusoidal signal may be subjected to nonlinear effects in which possible harmonic frequency components are generated. In such an environment, we may want to estimate (track) the signal´s fundamental frequency as well as any harmonic frequencies. Using a secondorder notch filter to estimate fundamental and harmonic frequencies is insufficient since it only accommodates one frequency component. On the other hand, applying a higher-order infinite impulse response (IIR) notch filter may not be efficient due to adopting multiple adaptive filter coefficients. In this article, we present a novel adaptive harmonic IIR notch filter with a single adaptive coefficient to efficiently perform frequency estimation and tracking in a harmonic frequency environment. Furthermore, we devise a simple scheme to select the initial filter coefficient to insure algorithm convergence to its global minimum error.