KFU. Card publication. How to reduce reproducible measurements to an ideal experiment?

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FEDERAL UNIVERSITY

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HOW TO REDUCE REPRODUCIBLE MEASUREMENTS TO AN IDEAL EXPERIMENT?

Form of presentation

Articles in Russian journals and collections

Year of publication

2014

Язык

русский

Authors, employees of KFU

Nigmatullin Ravil Rashidovich, author

Osokin Sergey Igorevich, author

Rakhmatullin Rafail Mansurovich, author

Bibliographic description in the original language

Nigmatullin R.R. How to reduce reproducible measurements to an ideal experiment? / R.R. Nigmatullin, R.M. Rakhmatullin, S.I. Osokin // Magn. Reson. Solids (Electr.J.). — 2014. — V.16. — № 2. — P. 14203–14221.

Annotation

Is it possible to suggest a general theory for consideration of reproducible data that are measured in many experiments? One can prove that successive measurements have a memory and this important fact allows separate all data on two large classes: ideal experiments without memory and experiments with a memory. We introduce the concept of an intermediate model (IM) that helps to describe quantitatively a wide class of reproducible data. Experiments with memory require for their description the Prony's decomposition while experiments without memory are needed for their presentation the Fourier decomposition only. In other words, it means that a measured function extracted from reproducible data can have a universal description in the form of the amplitude-frequency response (AFR) that belongs to the generalized Prony's spectrum (GPS). It is shown also how real data distorted by the experimental equipment and how to eliminate these uncontrollable factors in order to reproduce approximately the conditions corresponding to ideal experiment. New and elegant solution of elimination of the apparatus (instrument) function is suggested. In an ideal case the decomposition coefficients belong to the Fourier transform and presentation of reproducible data in this form leads to the IM for this case. The suggested general algorithm allows considering many experiments from the unified point of view. The real example based on available electron paramagnetic resonance (EPR) data confirms this general concept. The unified “bridge” between the treated experimental data and a set of competitive hypothesis that pretend for their description is discussed. The results obtained in this paper help to put forward a new paradigm in data/signal processing.

Keywords

Fourier transform, Prony's decomposition, intermediate model, data/signal processing, EPR measurements with/without memory, apparatus function

The name of the journal

Magn. Reson. Solids (Electr. J.)

On-line resource for training course

http://dspace.kpfu.ru/xmlui/bitstream/handle/net/184979/F_MRSej_14203_removed.pdf?sequence=1&isAllowed=y

URL

http://mrsej.ksu.ru/contents/2014/MRSej_14203.pdf

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=85556&p_lang=2

Resource files

File name	Size (MB)	Format
F_MRSej_14203_removed.pdf	0,51	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Nigmatullin Ravil Rashidovich	ru_RU
dc.contributor.author	Osokin Sergey Igorevich	ru_RU
dc.contributor.author	Rakhmatullin Rafail Mansurovich	ru_RU
dc.date.accessioned	2014-01-01T00:00:00Z	ru_RU
dc.date.available	2014-01-01T00:00:00Z	ru_RU
dc.date.issued	2014	ru_RU
dc.identifier.citation	Nigmatullin R.R. How to reduce reproducible measurements to an ideal experiment? / R.R. Nigmatullin, R.M. Rakhmatullin, S.I. Osokin // Magn. Reson. Solids (Electr.J.). — 2014. — V.16. — № 2. — P. 14203–14221.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=85556&p_lang=2	ru_RU
dc.description.abstract	Magn. Reson. Solids (Electr. J.)	ru_RU
dc.description.abstract	Is it possible to suggest a general theory for consideration of reproducible data that are measured in many experiments? One can prove that successive measurements have a memory and this important fact allows separate all data on two large classes: ideal experiments without memory and experiments with a memory. We introduce the concept of an intermediate model (IM) that helps to describe quantitatively a wide class of reproducible data. Experiments with memory require for their description the Prony's decomposition while experiments without memory are needed for their presentation the Fourier decomposition only. In other words, it means that a measured function extracted from reproducible data can have a universal description in the form of the amplitude-frequency response (AFR) that belongs to the generalized Prony's spectrum (GPS). It is shown also how real data distorted by the experimental equipment and how to eliminate these uncontrollable factors in order to reproduce approximately the conditions corresponding to ideal experiment. New and elegant solution of elimination of the apparatus (instrument) function is suggested. In an ideal case the decomposition coefficients belong to the Fourier transform and presentation of reproducible data in this form leads to the IM for this case. The suggested general algorithm allows considering many experiments from the unified point of view. The real example based on available electron paramagnetic resonance (EPR) data confirms this general concept. The unified “bridge” between the treated experimental data and a set of competitive hypothesis that pretend for their description is discussed. The results obtained in this paper help to put forward a new paradigm in data/signal processing.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Fourier transform	ru_RU
dc.subject	Prony's decomposition	ru_RU
dc.subject	intermediate model	ru_RU
dc.subject	data/signal processing	ru_RU
dc.subject	EPR measurements with/without memory	ru_RU
dc.subject	apparatus function	ru_RU
dc.title	How to reduce reproducible measurements to an ideal experiment?	ru_RU
dc.type	Articles in Russian journals and collections	ru_RU