Fitting Data Containing Multiple Exponentials Using Functionals Derived from Finite Laplace Transforms of Time Moments of the Data

Abstract

Functionals derived from the finite Laplace transforms of time moments of experimental data are used to fit these data to exponential functions. The functionals provide linear relationships for individually determining parameter values successively. This new and unique fitting method is first derived and then applied to data containing up to four exponentials to demonstrate its capabilities. Advantages of this fitting procedure include the following. (1) Parameters of the fit can be determined from the data region where they are most important by a wide verity of methods, including conventional ones. (2) Fitting algorithms are available that are simple to program; use conventional “stripping techniques”; are quite robust; and have been tested for a wide range in the number of data points, statistical errors, data ranges, and parameter values. (3) Fitting algorithms are included that use the conventional correlation coefficient of two expressions to fit data with even or uneven time intervals. (4) Decay constants and their associated magnitudes are determined separately and independently from different functionals. (5) Each iteration of the fit requires relatively few computations, usually only selected integrals, which can be completed quite rapidly. (6) Parameter errors can be estimated by conventional techniques.