Abstract
It is shown that a useful generalized linear filter W 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 in W. In turn, from this filter one determines a {open_quotes}Hamiltonian{close_quotes} H. The eigenvectors and eigenvalues of this Hamiltonian are evaluated. For A {open_quotes}good{close_quotes} experiment there is one small eigenvalue, and the rest are {approximately} 1. The W 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 of W 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 developments.
