Application of generalized linear filters in data analysis

Abstract

It is shown that a useful generalized linear filterW can be constructed from experimental data. The data are divided into many experiments and this ensemble is used to calculate the autocorrelation functions which appear inW. In turn, from this filter one determines a “Hamiltonian” ℋ. The eigenvectors and eigenvalues of this Hamiltonian are evaluated. For a “good” experiment there is one small eigenvalue, and the rest are ≈1. TheW so determined usefully reduces the noise in a new data set. The presence of two or more small eigenvalues indicates that the experimental data contains more than a single signal. The action ofW on selected members of the ensemble, and/or new data sets, extracts the different signals with, again, a useful noise reduction. Both computer simulations and real positron annihilation data are used to illustrate these development.