Detection of quasi-periodic processes in repeated measurements: New approach for the fitting and clusterization of different data

• New algorithm for detection of the quasi-periodic processes (QP) is suggested.
• The physical meaning of the generalized Prony’s decomposition is found.
• The analysis of the EPR data confirms the basic positions of new approach.
• The detection of the QP processes open new possibilities in analysis of different complex systems.

Many experimentalists were accustomed to think that any independent measurement forms a non-correlated measurement that depends weakly from others. We are trying to reconsider this conventional point of view and prove that similar measurements form a strongly-correlated sequence of random functions with memory. In other words, successive measurements “remember” each other at least their nearest neighbors. This observation and justification on real data help to fit the wide set of data based on the Prony’s function. The Prony’s decomposition follows from the quasi-periodic (QP) properties of the measured functions and includes the Fourier transform as a partial case. New type of decomposition helps to obtain a specific amplitude–frequency response (AFR) of the measured (random) functions analyzed and each random function contains less number of the fitting parameters in comparison with its number of initial data points. Actually, the calculated AFR can be considered as the generalized Prony’s spectrum (GPS), which will be extremely useful in cases where the simple model pretending on description of the measured data is absent but vital necessity of their quantitative description is remained. These possibilities open a new way for clusterization of the initial data and new information that is contained in these data gives a chance for their detailed analysis. The electron paramagnetic resonance (EPR) measurements realized for empty resonator (pure noise data) and resonator containing a sample (CeO2 in our case) confirmed the existence of the QP processes in reality. But we think that the detection of the QP processes is a common feature of many repeated measurements and this new property of successive measurements can attract an attention of many experimentalists.