ellibsЭлектронные библиотекиRussian Digital Libraries Journal1562-5419Казанский (Приволжский) федеральный университет10.26907/1562-5419-2025-28-2-378-397ellibs-551Research ArticleСтатьиНовые возможности преобразования Фурье: как описать произвольный частотно-фазовый модулированный сигнал?New Possibilities of the Fourier Transformation: How to Describe an Arbitrary Frequency-Phase Modulated Signal?НигматуллинРавиль РашидовичNigmatullinRaoul Rashidovichrenigmat@gmail.comЛитвиновАлександр АлексеевичLitvinovAlexander Alekseevichsharebox@bk.ruОсокинСергей ИгоревичOsokinSergey Igorevichs.osokin@it.kfu.ruКазанский национальный исследовательский университет им. А.Н. ТуполеваKazan National Research Technical University (KNRTU-KAI)Казанский (Приволжский) федеральный университетKazan (Volga region) Federal University202528052025282378–397Copyright © Нигматуллин Р.Р., Литвинов А.А., Осокин С.И., 20252025Нигматуллин Р.Р., Литвинов А.А., Осокин С.И.Nigmatullin R.R., Litvinov A.A., Osokin S.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://ellibs.elpub.ru/jour/article/view/551

В работе построено преобразование любого произвольного сигнала в строго периодическую форму, которое позволяет применять обычное преобразование Фурье для аппроксимации уже преобразованного сигнала. Наиболее интересным приложением (по мнению авторов) является аппроксимация сигналов с частотно-фазовой модуляцией, которые фактически находятся внутри найденного преобразования. Это новое преобразование будет полезным для описания откликов различных сложных систем, когда отсутствует обычная модель описания. В качестве доступных данных мы рассматриваем метеоданные, соответствующие измерениям концентрации метана (CH4) в атмосфере в течение 4 недель наблюдений. Было важно рассмотреть интегральные (кумулятивные) данные и найти их амплитудно-частотную характеристику (АЧХ). Если рассматривать каждый столбец как сигнал с частотно-фазовой модуляцией, то АЧХ можно оценить с помощью преобразования Фурье, период которого равен 2π, что справедливо для любого анализируемого случайного сигнала. Такое «универсальное» преобразование Фурье позволяет описать широкий набор случайных сигналов и сравнить их между собой по АЧХ. Эти новые возможности традиционного Фурье-анализа позволяют преобразованию Фурье стать еще более востребованным инструментом в арсенале методов, используемых исследователями в области обработки данных.

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 actually located inside the found transformation. This new transformation will be useful for application of the responses of different complex systems when an ordinary model is absent. As an available data we consider meteo-data corresponding to measurements of methane concentration (CH4) in atmosphere during 4 weeks of its observation. For us it is important to consider the integral (cumulative) data and find their amplitude-frequency response (AFR). If one considers each column as frequency-phase modulated signal, then AFR can be evaluated with the help of F-transformation that has the period equals 2p that is valid for any analyzed random signal. This "universal" F-transformation allows to fit a wide set of random signals and compare them with each other in terms of their AFRs. 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 data processing area.

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The authors declare that there are no conflicts of interest present.