Kazan Federal University Digital Repository

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

Show simple item record

dc.contributor.author Nigmatullin R.
dc.contributor.author Rakhmatullin R.
dc.date.accessioned 2018-09-18T20:12:45Z
dc.date.available 2018-09-18T20:12:45Z
dc.date.issued 2014
dc.identifier.issn 1007-5704
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/137607
dc.description.abstract 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. © 2014 Elsevier B.V.
dc.relation.ispartofseries Communications in Nonlinear Science and Numerical Simulation
dc.subject The generalized Prony's spectrum (GPS)
dc.subject The quasi-periodic (QP) process
dc.subject The repeated EPR measurements
dc.title Detection of quasi-periodic processes in repeated measurements: New approach for the fitting and clusterization of different data
dc.type Article
dc.relation.ispartofseries-issue 12
dc.relation.ispartofseries-volume 19
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 4080
dc.source.id SCOPUS10075704-2014-19-12-SID84901953336


Files in this item

This item appears in the following Collection(s)

  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

Show simple item record

Search DSpace


Advanced Search

Browse

My Account

Statistics