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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.

We propose and test a new method of multiexponential transient signal analysis. The method based on cepstral deconvolution is fast and computationally inexpensive. The multiexponential signal is initially converted to a deconvolution model using Gardners' transformation after which the proposed method is used to deconvolve the data. Simulation and experimental results indicate that this method is good for determining the number of components but performs poorly in accurately estimating the decay rates. Influence of noise is not considered in this paper.

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-Noise reduction in deconvolution process has been a challenge to researchers in the field of signal processing. The problem is ill-posed and various algorithms have been developed to reduce noise enhancement. The effect of using multiple noise-compensating parameters in the deconvolution of multiexponential signals is considered in this paper. Three parameters are simultaneously adjusted to obtain optimal reduction in noise. It is shown that this approach performs better than a single parameter approach.