Numerical transformations of wide-range time- and frequency-domain relaxational spectra

A numerical method is presented, which allows the calculation of distribution functions for relaxational systems from measured time-domain and frequency-domain spectra. The method is a further development of an earlier published algorithm to compute distribution functions from time-domain measurements. Besides the back-transform of time and frequency data, the new algorithms also allow the numerical calculation of the Kramers–Kronig relations and a Fourier transform using the distribution domain. A presumed distribution is altered and adjusted iteratively by the comparison of data calculated from the assumed spectrum with the measured data. A smoothing procedure is carried out to gain stability against noise.