"Universal" Fitting Function for Quantitative Description of Quasi-Reproducible Measurements

In this paper the authors are trying to justify the following statement: is there a general platform (it is defined as an intermediate model (IM)) for description of a wide class of quasi-reproducible (QR) experiments? Under QR experiments we understand the set of measurements when during a measurement cycle they can be varied significantly under the influence of uncontrollable factors. If this general platform exists then it facilities the analysis of experiments associated with properties of complex systems, when the "best-fit function" that follows from the microscopic model is absent. This platform will bring a certain profit for a competitive/alternative theory. If the fitting function obtained from the theory looks very complicated then it can be expressed in terms of the IM and the parameters of this IM are expressed in terms of the generalized Prony spectrum. The physical meaning of the Fourier transform that used as the fitting function is explained also. It corresponds to an "ideal experiment" when all measurements during the experimental cycle are fully identical to each other. The new formulae for elimination of the apparatus functions are suggested. They help to evaluate the influence of uncontrollable factors and at certain conditions reduce the measured data to an "ideal experiment". As a nontrivial example we consider the fit of the single heartbeat (HB) recorded from anonymous persons. We took the ECG data from the reliable Internet resource PhysioNet Bank (http://physionet.org/cgi-bin/atm/ATM). The obtained results of its nontrivial application demonstrate its effectiveness in quantitative description of the ECG data in the frame of the suggested theory. We do hope that the quantitative description of the single heartbeat will find an application in the modern cardiology.