Polynomial predictive filters: complementing technique to fuzzy filtering

Dealing with impulsive noise remains one of the great engineering challenges due to the difficulties in modeling and filtering impulsive noise. Since impulsive noise is, in general, a non-stationary stochastic process, neural networks and fuzzy systems have been applied to deal with it. In many cases, however, the underlying primary signal is smoothly changing. Therefore, a more simple approach, namely polynomial predictive filtering, can successfully be applied instead of soft computing methods. In this paper, we present a filtering system which consists of a cascade of a median filter and a polynomial predictive filter. The proposed system is capable of removing the strong impulses that are present in the polynomial-like input signal without introducing a disturbing delay. The simulation results are compared with the corresponding results obtained by applying fuzzy filtering. Finally, we consider an interesting concept called smoothness of a signal; we will show that the choice of feasible filtering approach and its parameters is dependent on the degree of smoothness of the signal to be filtered.