Suboptimal filtering and nonlinear time scale transformation for the analysis of multiexponential decays

Abstract—Multiexponential decays may contain time-constants differing in several orders of magnitudes. In such cases, uniform sampling results in very long records featuring a high degree of oversampling at the final part of the transient. Here, we analyze a nonlinear time scale transformation to reduce the total number of samples with minimum signal distortion, achieving an important reduction of the computational cost of subsequent analyses. We propose a time-varying filter whose length is optimized for min-imum mean square error. Index Terms—Data reduction, Gardner transform, multiexpo-nential decay, noise, nonuniform sampling, transients