An Appraisal of Gardner Transform-Based Methods of Transient Multiexponential Signal Analysis

Abstract

There are several problems in applied science in which experimental observations can be accurately represented by a sum of exponential decay functions in which the amplitudes, decay rates and number of components have different physical interpretations and need to be estimated. A parameter estimation technique of multicomponent exponential functions that has undergone many modifications is the Gardner transform in which a nonlinear transformation is used to convert the data signal into a convolution model containing the parameters of interest. Modifications of this early technique include modification of the original transform or deconvolution procedure and additional processing of the deconvolved data to obtain better estimates of the desired parameters. This paper presents an appraisal of Gardner transform and its variants. It discusses major modifications and their implications to the overall results of analysis.