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.