FUNCTIONAL CONVERSION OF SIGNALS IN THE STUDY OF RELAXATION PHENOMENA

The processing of monotonic signals that appeared in studying the rela xation phenomena is considered. These signals are generalized as relax ation signals and are represented by infinite functions with infinite spectra having derivatives tending to zero, when the argument goes to infinity. A logarithmic sampling where a distance between samples incr eases according to a geometric progression is found to be optimal for the relaxation signals. A periodic spectrum in the Mellin transform do main is shown to have a logarithmically sampled signal. Conversion of the relaxation signals based on carrying out direct and inverse integr al transforms of the first kind with kernels depending on the division or product of arguments is offered by digital filtering on the logari thmically transformed argument domain. A theory of digital functional filters (DFFs) with the logarithmic sampling is developed. Conditions of an exact performance of the integral transform are found. A method of regularization is developed for integral transforms being ill-condi tioned where a geometric progression ratio is used as a regularization parameter. A multicriterial optimization method is developed for opti mal DFF design based on identification of a discrete system where theo retical functions interrelated with each other by the desired integral transform are used as input and output signals.