Journal ArticleDOI
An eigenfunction expansion method for the analysis of exponential decay curves
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TLDR
In this article, a method is developed for the analysis of data composed of random noise, plus an unknown constant "baseline", plus a sum (or an integral over a continuous distribution) of exponential decay functions.Abstract:
A method is developed for the analysis of data composed of random noise, plus an unknown constant ’’baseline,’’ plus a sum (or an integral over a continuous distribution) of exponential decay functions. It is based on the expansion of the solution of a Fredholm integral equation of the first kind in the eigenfunctions of the kernel. In contrast to the Fourier transform solution [Gardner et al., J. Chem. Phys. 31, 978 (1959)], the finite time range of the data is exactly accounted for, and no extrapolation or iteration is necessary. A computer program is available for the analysis of sums of exponentials. It is completely automatic in that the only input are the data (not necessarily in equal intervals of time); no potentially biased initial estimates of either the number or values of the amplitudes and decay constants are needed. These parameters and their standard deviations are decided with a linear hypothesis test corrected approximately for nonlinearity. Tests with simulated two‐, three‐, and four‐com...read more
Citations
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Observations of radiative transitions between the doubly excited 2p43s3p and 2p43s3d configurations in Ne-like S VII and Cl VIII
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References
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Journal ArticleDOI
Handbook of Mathematical Functions
Journal ArticleDOI
A Fourier method for the analysis of exponential decay curves
TL;DR: A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions.
Journal ArticleDOI
Method for the Analysis of Multicomponent Exponential Decay Curves
TL;DR: In this article, a mathematical approach based on the inversion of the Laplace integral equation by a method of Fourier transforms was proposed to estimate the physically significant parameters Ni and λi. The results of the analysis appeared in the form of a frequency spectrum.