ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Non-Orthogonal Amplitude-Frequency Analysis of the Smoothed Signals(NAFASS): Dynamics and the Fine Structure of the Sunspots

Journal of Applied Nonlinear Dynamics 4(1) (2015) 67--80 | DOI:10.5890/JAND.2015.03.006

Nigmatullin R.R; Toboev V.A.

$^{1}$ Kazan National Research Technical University (KNRTU-KAI), Kazan, Tatarstan, Russia,

$^{2}$ Department of Mathematics, Chuvash State University, Cheboksary, Russian Federation

Abstract

The basic aim of the given paper is presentation of the basic principles of the new method defined as Non-orthogonal Amplitude Frequency Analysis of the Smoothed Signals (NAFASS). The new method is based on linear principle for the strongly-correlated variables and presentation of nonlinear signals. We demonstrate the possibilities of the NAFASS approach on analysis of real data related to dynamics and the fine structure of the Solar activity

Acknowledgments

This research is realized in the frame of the program accepted as a basic part of the state enumeration of the problems that are contained in the list of the Ministry of Education and Science of the Russian Federation. One of us (RRN) wants to note that this problem enters as a basic component of the R&D joint-lab program organized between the Jinan University (Guangzhou, PRC) and Kazan National Research Technical University (KNRTU-KAI, Kazan, Russian Federation).

References

1.  [1] Bloomfield, P. (1976), Fourier Analysis of Time Series: An Introduction, Wiley, New-York.
2.  [2] Oppenheim, A.V., Willsky, A.S., and Nawab, S.H. (1997), Signals and Systems. (2nd edition), Prentice-Hall, Englewood Cliffs, NJ.
3.  [3] Bendat, J.S. and Pirsol, A.G. (1986), Random Data: Analysis and Measurement Procedures. (2nd edition), Wiley, New York.
4.  [4] Papoulis, A. (1977), Signal Analysis, McGraw-Hill, New York.
5.  [5] Brillinger, D.R. (1975), Time series. Data analysis and theory, Rinehart and Winston, Inc., Holt.
6.  [6] Lathi, B.P. (1998), Signal Processing and Linear Systems, Cambridge, Carmicheal, CA.
7.  [7] Marple, L.S. Jr. (1987), Digital spectral analysis with applications, Prentice Hall, Englewood Cliffs, NJ.
8.  [8] Oppenheim, A.V. and Schafer, R.W. (1989), Discrete time Signal Processing, Prentice-Hall, Englewood Cliffs, NJ.
9.  [9] Korn G.A. and Korn T. (2000), Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review, Dover Publications.
10.  [10] Little, J.N and Shure, L. (1992), Signal Processing Toolbox for Use with MATLAB, The Math Works, Inc., Natick, MA.
11.  [11] Eskov, E.K. and Toboev, V.A. (2010), Analysis of Statistically Homogeneous Fragments of Acoustic Noises Generated by Insect Colonies, Biophysics, 55(1), 92-103.
12.  [12] Nigmatullin, R.R and Toboev V.A. (2009), Non-invasive methods of extraction of significant informative components and clusterization of acoustic noises of an arbitrary nature. Nelineyny Mir, (Nonlinear World), 7(5), 348-354. (in Russian).
13.  [13] Toboev V.A and Tolstov M.S. (2011), The calculation of harmonic discrete spectra of short signals, Nelineyny Mir, (Nonlinear World). 9(9), 611-618. (In Russian).
14.  [14] Nigmatullin, R.R. (2012), The fluctuation metrology based on Prony's spectroscopy (II), The Journal of Applied Nonlinear Dynamics, 1(3), 207-225.
15.  [15] Nigmatullin, R.R., Khamzin, A.A., and Machado, J.T. (2014), Detection of quasi-periodic processes in complex systems: how do we quantitatively describe their properties? Physica Scripta, 89 015201 (11pp).
16.  [16] Nigmatullin,R.R., Osokin, S.I., Baleanu, D., Al-Amri, S., Azam, A., Memic A. (2014), The First Observation of Memory Effects in the InfraRed (FT-IR) Measurements: Do Successive Measurements Remember Each Other? PLoS ONE, Open access journal, April 9 (4) e94305.
17.  [17] Nigmatullin, R.R. (2010) Universal distribution function for the strongly-correlated fluctuations: general way for description of random sequences. Communications in Nonlinear Science and Numerical Simulation. 15, 637-647.
18.  [18] Nigmatullin, R.R. (2006), The statistics of the fractionalmoments: Is there any chance to "read quantitatively" any randomness? Journal of Signal Processing, 86, 2529-2547.
19.  [19] Nigmatullin, R.R., Osokin, S.I. and Toboev, V.A. (2011), NAFASS: Discrete spectroscopy of random signals, Chaos, Solitons & Fractals, 44(4-5), 226-240.
20.  [20] Nigmatullin, R.R. (2012), Is it possible to replace the probability distribution function by its Prony's spectrum? (I) The Journal of Applied Nonlinear Dynamics, 1(2), 173-194.
21.  [21] Nigmatullin, R.R. (2008), Strongly Correlated Variables and Existence of the Universal Distribution Function for Relative Fluctuations, Physics of Wave Phenomena, 16 (2), 119-145.
22.  [22] Nigmatullin, R.R. (1998), Eigen-Coordinates: New method of identification of analytical functions in experimental measurements, Applied Magnetic Resonance, 14, 601-633.
23.  [23] SIDC-Solar Influences Data analysis Center . http://sidc.oma.be/DATA/monthssn.dat (cited on 24.10.2014).
24.  [24] Gnedyshev M.N., Ol'A.I. (1948), About 22 year cycle of the Solar activity Astronomic Journal. 25, 18-20. (In Russian).
25.  [25] Usoskin, I. G. (2013), A history of solar activity over millennia, Living Reviws in Solar Physics, 5, 1-88.
26.  [26] Hoyt, D.V. and Schatten, K.H. The Role of the Sun in Climate Change. Ozford University Press, New York, 1997.
27.  [27] Li, K.J., Gao, P.X. and Su, T.W. (2005), The Schwabe and Gleissberg Periods in the Wolf Sunspot Numbers and the Group Sunspot Numbers, Solar Physics, 229(1), 181-201.