| Form of presentation | Articles in international journals and collections |
| Year of publication | 2025 |
| Язык | английский |
|
Litvinov Aleksandr Alekseevich, author
Osokin Sergey Igorevich, author
|
|
Nigmatullin Ravil Rashidovich, author
|
| Bibliographic description in the original language |
Nigmatullin R.R. New Possibilities of the Fourier Transformation: How to Describe an Arbitrary Frequency-Phase Modulated Signal?/R.R. Nigmatullin, A.A. Litvinov, S.I. Osokin//Lobachevskii Journal of Mathematics. - 2025. - Vol.46. - No.5. - PP. 2406-2414. |
| Annotation |
In this paper, the authors found a transformation that is valid for any arbitrary signal. This transformation is strictly periodical and, therefore, it allows to apply the ordinary F-transformation for the fitting of the transformed signal. The most interesting application (in accordance with the author's opinion) is the fitting of the frequency-phase modulated signals that located actually inside the found transformation. This new transformation will be useful for application of the responses of different complex systems when a particular model is absent. As available data, we consider cosmic microwave background data (CMB) associated with the background temperature fluctuations near T = 2.725 K. These electro-magnetic (EM) fluctuations of the early Universe were measured at the wide frequency range 30–857 GHz. In this paper, we analyzed the measured data at 353 GHz corresponding to the taken zero pixels. Other details are described in the second section of the paper. This squared matrix corresponding to the measured data contains 2047 lines × 2047 columns. If one considers each column as frequency-phase modulated signal, then amplitude frequency response can be evaluated with the help of F-transformation that has the period equals 2π that is valid for any analyzed random signal. These “universal” behavior allows to fit a wide set of random signals and compare them with each other in terms of their amplitude-frequency responses (AFR). Concluding the abstract, one can say that these new possibilities of the traditional F-analysis will serve as a common tool in the armory of the methods used by researchers in the data processing area. |
| Keywords |
Fourier transformation (F-transformation), Fourier analysis (F-analysis), Fourier series, cosmic microwave background data, electro-magnetic fluctuations, amplitude-frequency responses, fitting of the frequency-phase modulated signals |
| The name of the journal |
Lobachevskii Journal of Mathematics
|
| URL |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-105016492884&doi=10.1134%2FS1995080225605636&partnerID=40&md5=9bc2574ad305a23e496a85c28b9b4ed1 |
| Please use this ID to quote from or refer to the card |
https://repository.kpfu.ru/eng/?p_id=317939&p_lang=2 |
| Resource files | |
|
|
Full metadata record  |
| Field DC |
Value |
Language |
| dc.contributor.author |
Litvinov Aleksandr Alekseevich |
ru_RU |
| dc.contributor.author |
Osokin Sergey Igorevich |
ru_RU |
| dc.contributor.author |
Nigmatullin Ravil Rashidovich |
ru_RU |
| dc.date.accessioned |
2025-01-01T00:00:00Z |
ru_RU |
| dc.date.available |
2025-01-01T00:00:00Z |
ru_RU |
| dc.date.issued |
2025 |
ru_RU |
| dc.identifier.citation |
Nigmatullin R.R. New Possibilities of the Fourier Transformation: How to Describe an Arbitrary Frequency-Phase Modulated Signal?/R.R. Nigmatullin, A.A. Litvinov, S.I. Osokin//Lobachevskii Journal of Mathematics. - 2025. - Vol.46. - No.5. - PP. 2406-2414. |
ru_RU |
| dc.identifier.uri |
https://repository.kpfu.ru/eng/?p_id=317939&p_lang=2 |
ru_RU |
| dc.description.abstract |
Lobachevskii Journal of Mathematics |
ru_RU |
| dc.description.abstract |
In this paper, the authors found a transformation that is valid for any arbitrary signal. This transformation is strictly periodical and, therefore, it allows to apply the ordinary F-transformation for the fitting of the transformed signal. The most interesting application (in accordance with the author's opinion) is the fitting of the frequency-phase modulated signals that located actually inside the found transformation. This new transformation will be useful for application of the responses of different complex systems when a particular model is absent. As available data, we consider cosmic microwave background data (CMB) associated with the background temperature fluctuations near T = 2.725 K. These electro-magnetic (EM) fluctuations of the early Universe were measured at the wide frequency range 30–857 GHz. In this paper, we analyzed the measured data at 353 GHz corresponding to the taken zero pixels. Other details are described in the second section of the paper. This squared matrix corresponding to the measured data contains 2047 lines × 2047 columns. If one considers each column as frequency-phase modulated signal, then amplitude frequency response can be evaluated with the help of F-transformation that has the period equals 2π that is valid for any analyzed random signal. These “universal” behavior allows to fit a wide set of random signals and compare them with each other in terms of their amplitude-frequency responses (AFR). Concluding the abstract, one can say that these new possibilities of the traditional F-analysis will serve as a common tool in the armory of the methods used by researchers in the data processing area. |
ru_RU |
| dc.language.iso |
ru |
ru_RU |
| dc.subject |
Fourier transformation (F-transformation) |
ru_RU |
| dc.subject |
Fourier analysis (F-analysis) |
ru_RU |
| dc.subject |
Fourier series |
ru_RU |
| dc.subject |
cosmic microwave background data |
ru_RU |
| dc.subject |
electro-magnetic fluctuations |
ru_RU |
| dc.subject |
amplitude-frequency responses |
ru_RU |
| dc.subject |
fitting of the frequency-phase modulated signals |
ru_RU |
| dc.title |
New Possibilities of the Fourier Transformation: How to Describe an Arbitrary Frequency-Phase Modulated Signal? |
ru_RU |
| dc.type |
Articles in international journals and collections |
ru_RU |
|
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