Optimal filtering of nerve singnals

Recording from multiple electrodes at different sites along a peripheral nerve permits the application of powerful filtering methods to extract the activity of populations of fibres within the nerve which differ in temporal or spectral characteristics. The design of optimal linear filters is initially treated as a general problem in the calculus of variations in which the signals from one population of nerve fibres are extracted so as to minimize those from a second population of nerve fibres or from other sources (noise). A particularly important application arises when the signals at two electrodes are related by weighting functions. In the simplest example the weighting function represents the time delay for nerve impulses to conduct from one electrode to the other, but explicit results are also derivable when there are a range of conduction delays with probabilities distributed according to well-known functions such as the sinc² function.This work was partially supported by the National Research Council of Canada and Medical Research Council of Canada by Grant NRC A-4345 to MNO and Grant MRC MA-3307 to RBS through the University of Alberta