The combined use of the improved methods of Gardner and Prony for the qualitative and quantitative analysis of multicomponent decay curves

Two complementary methods, the improved method of Gardner et al. and of Prony for the analysis of multicomponent decay curves, are presented. The improved method of Gardner et al. can be applied to determine the number of components and to estimate the decay constants. These can then be quantified together with the pre-exponential factors using the recurrence version of Pronyʹs improved method. Computer implementations of these methods are described. Their performance is evaluated on simulated decay curves in the absence and presence of Poisson distributed noise, as well as on experimental decay curves obtained from fluorescence, solid state free induction decay (1H NMR), and radioactivity measurements. Guidelines for experiments are formulated in order to obtain the best results in the sequential data analyses.