Robust Notch Filtering by Combining Adaptation in both Time and Frequency

Abstract

A fully adaptive infinite impulse response (IIR) notch filter has been proposed before with a very good tracking property over a certain frequency range [7,8]. It is shown that when the frequency to be notched is closed to DC or the Nyquist frequency (fr,) the performance of the IIR notch filter is degraded. A finite impulse response (FIR) notch filter with equal number ofcoefficients exhibits a reversed performance: the tracking performance is worse than the IIR notch filter in those frequencies far from DC and fn but better than the IIR notch filter in those frequencies close to either DC orfn.Hence, a combination of these two filters is proposed in this paper to improve the tracking performance of the notch filter over the total range of frequencies. Computer simulations show the improved performance of the combined adaptive filter. The design is also simple in computation and robust in tracking a time-varying sinusoidal signal.

Stochastic Search Methods to Improve the Convergence of Adaptive Notch Filters

“…Regions with parameter and outside of the correct frequency are extremely flat and can be considered as local minima, which attract the ANF frequency miss-lock. This problem is especially prevalent when the frequency is too low or too high [7]. To overcome the non-quadratic nature of the error surface, we can employ a classical technique called stochastic search (or random search), with a modification for our situation.…”

“…At time : A serious problem associated with the Nehorai ANF in specific, and any IIR structure in general, is the well known non-absolute convergence problems [7]. The underlying issue is the non-quadratic error surface which may have local minima.…”

“…This property is a consequence of the filter's non-quadratic error surface due to the inherent IIR structure [6]. This shortcoming leads to the situation of frequency miss-lock when the filter adapts to a local minimum of the error surface, which can happen occasionally [7]. Thus, it is always an important aspect in Adaptive Notch Filter design to improve the convergence rate, such as the lattice-based approach in [8].…”

A Frequency Tracking Method Based on Improved Adaptive Notch Filter for Coriolis Mass Flowmeter

“…Due to their IIR inherent structure, ANFs are known to have non-absolute convergence problem [9] . Fig.…”