Digital estimators of relaxation spectra

Determination of the distribution of relaxation times (DRT) from a wide variety of the time- and the frequency-domain material functions, such as polarization current and charge, real and imaginary parts of complex dielectric permittivity and complex dielectric modulus, the appropriate mechanical and magnetic counterparts is generalized as a filtering problem on a logarithmic time or frequency scale. Algorithms of the appropriate digital DRT estimators are derived. A novel regularization strategy is proposed based on choosing sampling rate for the input data, which ensures acceptably low random error of the recovered spectra. Optimum frequency ranges and sampling rates are found for determination of the relaxation spectrum from the real part of complex permittivity and complex modulus. A multi-filter DRT recovery strategy is suggested by a bank of filters with different smoothing abilities.