Decomposition of Multicomponent Exponential Decays by Spectral Analytic Techniques

It is shown that multicomponent exponential decays can be analysed using a technique which produces a spectrum whose peaks correspond in amplitude and position to the various exponential components present in the data. This technique is analogous to the Fourier Transform which provides a spectrum of the frequency components (complex exponentials) of a signal. Three techniques—the Orthonormal Exponential Transform, the Inverse Laplace Transform and the Gardner Transform are examined and their relative effectiveness in producing the desired spectra from theoretically generated and experimental data is discussed. It is shown that the updated Gardner Transform can be Ilsed to analyse experimental multicomponent exponential decays.