High-resolution exponential analysis via regularized numerical inversion of Laplace transforms

The paper describes a new, robust method for the exponential analysis problem solving. In discrete case the regularizing operators of the inverse Laplace transformation are used for transformation of experimental data into a form that is more suitable for determination of decay rates and amplitudes. In the case of a continuous distribution a spectral function is obtained by regularized inverse Laplace transformation of the transient. The proposed method has advantages over known methods and is tolerant to the baseline offset. The results of numerical testing show that the proposed method can be used in high-resolution analysis for determination of spectral functions, decay rates and amplitudes from experimentally measured transients.