Abstract
An important element in relaxation-time analysis is the fitting of a decay curve to the sum of a series of exponential functions. In such a fitting process, the experimental error has a strong influence on the accuracy of the derived amplitudes and time constants. This has been explored by nonlinear least-squares fitting of computer-simulated data sets which include noise from a normal distribution, N(0.0, σ). Results from the analysis of the computer-simulated decay curves indicate that an S/N in the region of 1000:1 is necessary for three-exponential fittings to be carried out with confidence. Problems can arise when relaxation-decay curves are analyzed if the time constants describing the decay differ by factors of less than about two.
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