Non-Linear Effects in Adaptive Linear Prediction

When a conventional NLMS adaptive filter is used to predict a process, especially when predicting several samples ahead, non-linear effects can be observed. These non-linear effects produce adaptive filter performance that exceeds that of the conventional Wiener filter, and engenders weight behavior that is of a time-varying nature. After showing the existence of such non-linear effects, we show their relation to the difference between the structure of the optimal predictor and the structure used to model the data to be predicted. The nonlinear effects are stronger when the process to be predicted is more narrowband.