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Journal of Applied Nonlinear Dynamics 1(3) (2012) 207--226 | DOI:10.5890/JAND.2012.06.001

Raoul R. Nigmatullin

Theoretical Physics Department, Institute of Physics, Kazan Federal University, Kremlevskaya str., 18, 420008, Kazan, Russian Federation

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Abstract

The basic purpose of this paper is related to creation of the basis of new metrology based on quantitative analysis of the Prony’s spectra. The Prony’s spectroscopy gives a possibility to transform a wide class of multi-periodic and random signals (associated with a clearly expressed trend) to their amplitudefrequency response (AFR). For the strongly-correlated complex systems with memory the corresponding AFR is generated by a few initial frequencies that allow realizing the further compression of the initial random signal and reading it in terms of the limited number of quantitative parameters. This important peculiarity of the Prony’s spectroscopy allows in creating of a “universal” language for reading of different fluctuations and comparing them with each other. One interesting example of reading of the infinite sequences that are formed from the transcendental numbers (the Euler’s constant E = 2.71828... and number π = 3.14159...) is considered. The new elements that are added to calculation scheme/algorithm increase the stability and accuracy of the Prony’s spectra considered. In general, it opens new possibilities in creation of the basis of the fluctuation metrology that enables to read a wide class of random signals and compare them with other signals in terms of the quantitative parameters entering into the corresponding AFRs that, in turn, are governed by the corresponding distribution of frequencies.

Acknowledgments

This paper was written in the frame of the scientific research program that was accepted by Kazan Federal University for 2012 year “Dielectric spectroscopy and kinetics of complex systems”.

References

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