Autoassociative neural networks and noise filtering

We introduce linear autoassociative neural (AN) network filters for the removal of additive noise from one-dimensional (1-D) time series. The AN network will have a (2M+1)×L×(2M+1) architecture, and for M fixed, we show how to choose the optimal L value and output coordinate from square error estimates between the AN filter outputs and the clean series. The frequency response of AN filters are also studied, and they are shown to act as matched band filters. A noise variance estimate is also derived from this analysis. We numerically illustrate their behavior on two examples and also compare their theoretical performance with that of optimal Wiener filters.