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    New Possibilities of the Fourier Transformation: How to Describe an Arbitrary Frequency-phase Modulated Signal?

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    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.2406-241

    Труды XXIX Всероссийской открытой научной конференции (Казань, 30 июня–4 июля 2025 г.)

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    Труды XXIX Всероссийской открытой научной конференции (Казань, 30 июня–4 июля 2025 г.)В труды включены доклады, отражающие результаты исследований в области распространения радиоволн от километрового до субмиллиметрового диапазонов в различных средах; распространения широкополосных сигналов в средах с дисперсией; результаты дистанционного зондирования космического пространства, ионосферы, атмосферы и земных покровов в радио, ИК и оптическом диапазонах; радиофотоники; исследований нелинейных эффектов в ионосфере, возникающих при распространении радиоволн большой мощности: эффектов, проявляющихся в диапазоне радиочастот, связанных с атмосферным электричеством. Представленные в трудах новые научные результаты в области распространения радиоволн могут быть полезны специалистам по радиофизике, геофизике, радиосвязи, радиолокации и радионавигации, а также студентам, аспирантам и докторантам соответствующих специальностей.69

    New Method of Description of Eddy-Covariance Ecologic Data

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    In this paper, the authors propose the foundations of an original theory of quasi-reproducible experiments (QREs) based on the testable hypothesis that there exists an essential correlation (memory) between successive measurements. From this hypothesis, which the authors call for brevity as the verified partial correlation principle (VPCP), it can be proved that there exists a universal fitting function (UFF) for quasi-reproducible (QR) measurements. In other words, there is some common platform or bridge across which, figuratively speaking, a true theory (claiming to describe data from first principles or verifiable models) and an experiment offering this theory for verification of measured data, maximally cleaned from the influence of uncontrollable factors and apparatus/software function, meet. Actually, the proposed theory provides the potential researcher with a method of the purification of initial data, finally suggesting a curve that describes the data, is periodic, and is cleaned from a set of uncontrollable factors. The final curve corresponds to an ideal experiment. The proposed theory has been tested on eddy-covariance ecological data related to the content of CH4, CO2, and H2O in the local atmosphere, where the corresponding detectors for measuring of the desired gases content are located. For these tested eddy-covariance data associated with the presence of CH4, CO2, and H2O vapor in the atmosphere there is no simple hypothesis containing a minimal number of the fitting parameters, and, therefore, the fitting function that follows from this theory can serve as the only and most reliable quantitative description of this kind of data that belongs to the tested complex system. We should also note that the final fitting function that is removed from uncontrollable factors becomes purely periodic and corresponds to an ideal experiment. Applications of this theory to practical applications, its place among other alternative approaches (especially touching the professional interests of ecologists), and its further development are discussed in the paper.S15-S2

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