APPLICATION OF GENERALIZED LINEAR FILTERS IN DATA-ANALYSIS

It is shown that a useful generalized linear filter W can be construct ed from experimental data. The data are divided into many experiments and this ensemble is used to calculate the autocorrelation functions w hich appear in W. In turn, from this filter one determines a ''Hamilto nian'' H. The eigenvectors and eigenvalues of this Hamiltonian are eva luated. For a ''good'' experiment there is one small eigenvalue, and t he rest are approximately 1. The W' so determined usefully reduces the noise in a new data set. The presence of two or more small eigenvalue s indicates that the experimental data contains more than a single sig nal. The action of W on selected members of the ensemble, and/or new d ata sets, extracts the different signals with, again, a useful noise r eduction. Both computer simulations and real positron annihilation dat a are used to illustrate these developments.