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

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.

Fourier transform, random signal, frequency-phase modulated signal, amplitude-frequency response, complex systems, meteorological data, eddy covariance

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