Autoassociative neural networks and noise filtering

In this work, we will 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 (2 + 1) (2 + 1) architecture, and for fixed, we will show how to choose the optimal value and output coordinate from square error estimates between the AN filter outputs and the clean series. The frequency response of AN filters will also be studied, and they will be shown to act as matched band filters. A noise variance estimate will also be derived from this analysis. We will numerically illustrate their behavior on two examples and will also compare their theoretical performance with that of optimal Wiener filters.