On the Recovery and Resolution of Exponential Relaxation Rates from Experimental Data: A Singular-Value Analysis of the Laplace Transform Inversion in the Presence of Noise

The problem of numerical inversion of the Laplace transform is considered when the inverse function is of bounded, strictly positive support. The recent eigenvalue analysis of McWhirter and Pike for infinite support has been generalized by numerical calculations of singular values. A priori knowledge of the support is shown to lead to increased resolution in the inversion, and the number of exponentials that can be recovered in given levels of noise is calculated