Adaptive Harmonic IIR Notch Filters for Frequency Estimation and Tracking

Abstract

In many signal processing applications, adaptive frequency estimation and tracking of noisy narrowband signals is often required in communications, radar, sonar, controls, biomedical signal processing, and the applications such as detection of a noisy sinusoidal signal and cancellation of periodic signals. In order to achieve the objective of frequency tracking and estimation, an adaptive finite impulse response (FIR) filter or an adaptive infinite impulse response (IIR) notch filter is generally applied. Although an adaptive FIR filter has the stability advantage over an adaptive IIR notch filter, it requires a larger number of filter coefficients. In practical situations, an adaptive IIR notch filter (Chicharo & Ng, 1990; Kwan & Martin, 1989; Nehorai, 1985) is preferred due to its less number of filter coefficients and hence less computational complexity. More importantly, a second-order adaptive pole/zero constrained IIR notch filter (Xiao et al, 2001; Zhou & Li, 2004) can effectively be applied to track a single sinusoidal signal. If a signal contains multiple frequency components, then we can estimate and track its frequencies using a higher-order adaptive IIR notch filter constructed by cascading second-order adaptive IIR notch filters (Kwan & Martin, 1989). To ensure the global minimum convergence, the filter algorithm must begin with initial conditions, which require prior knowledge of the signal frequencies. However, in many practical situations, a sinusoidal signal may be subjected to nonlinear effects (Tan & Jiang, 2009a, 2009b) in which possible harmonic frequency components are generated. For example, the signal acquired from a sensor may undergo saturation through an amplifier. In such an environment, we may want to estimate and track the signal’s fundamental frequency as well as any harmonic frequencies. Using a second-order adaptive IIR 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 IIR notch filter may not be effective due to adopting multiple adaptive filter coefficients and local minimum convergence of the adaptive algorithm. In addition, monitoring the global minimum using a grid search method requires a huge number of computations, and thus makes the notch filter impractical in real time processing. Therefore, in this chapter, we propose and investigate a novel adaptive harmonic IIR notch filter with a single adaptive coefficient to efficiently perform frequency estimation and tracking in a harmonic frequency environment.