Discrete sums for the rapid determination of exponential decay constants

Abstract

Several computational methods are presented for the rapid extraction of decay time constants from discrete exponential data. Two methods are found to be comparably fast and highly accurate. They are corrected successive integration and a method involving the Fourier transform (FT) of the data and the application of an expression that does not assume continuous data. FT methods in the literature are found to introduce significant systematic error owing to the assumption that data are continuous. Corrected successive integration methods in the literature are correct, but we offer a more direct way of applying them which we call linear regression of the sum. We recommend the use of the latter over FT-based methods, as the FT methods are more affected by noise in the original data.