ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Pavlov A. N. Detection of information signals based on reconstruction of dynamical systems and discrete wavelet-transform. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 6, pp. 3-17. DOI: 10.18500/0869-6632-2008-16-6-3-17

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2008-16-6-3-17

Detection of information signals based on reconstruction of dynamical systems and discrete wavelet-transform

Autors: 
Pavlov Aleksej Nikolaevich, Saratov State University
Abstract: 

An approach to extract transmitted messages from the chaotic carrying signal is proposed based on the combination of dynamical systems reconstruction and the discrete wavelet-transform. It is shown that discrete wavelets allow one to increase the stability to noise of the detecting algorithm that deals with the reconstruction technique.

Key words: 
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Reference: 
  1. Cuomo KM, Oppenheim AV. Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett. 1993;71(1):65–68. DOI: 10.1103/PhysRevLett.71.65.
  2. Kocarev L, Halle KS, Eckert K, Chua LO, Parlitz U. Experimental demonstration of secure communications via chaotic synchronization. Int. J. Bifurcat. Chaos. 1992;2(3):709–713. DOI: 10.1142/S0218127492000823.
  3. Wu CW, Chua LO. A simple way to synchronize chaotic systems with applications to secure communication systems. Int. J. Bifurcat. Chaos. 1993;3(6):1619–1627. DOI: 10.1142/S0218127493001288.
  4. Parlitz U, Chua LO, Kocarev L, Halle KS, Shang A. Transmission of digital signals by chaotic synchronization. Int. J. Bifurcat. Chaos. 1992;2(4):973–977. DOI: 10.1142/S0218127492000562.
  5. Cuomo KM, Oppenheim AV, Strogatz SH. Synchronization of Lorenz-based chaotic circuits with application to communications. IEEE Trans. Circuits Syst. 1993;40(10):626–633. DOI: 10.1109/82.246163.
  6. Dedieu H, Kennedy MP, Hasler M. Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuit. IEEE Trans. Circuits Syst. 1993;40(10):634–642. DOI: 10.1109/82.246164.
  7. Parlitz U. Estimating model parameters from time series by autosynchronization. Phys. Rev. Lett. 1996;76(8):1232–1235. DOI: 10.1103/physrevlett.76.1232.
  8. Parlitz U, Kocarev L. Multichannel communication using autosynchronization. Int. J. Bifurcat. Chaos. 1996;6(3):581–588. DOI: 10.1142/S0218127496000278.
  9. Dmitriev AS, Panas AI. Dynamic Chaos: New Carriers of Information for Communication Systems. Moscow: Fizmatlit; 2002. 252 p. (in Russian).
  10. Starkov SO, Yemetz SV. Digital communication systems, using chaos. In: 1997 1st International Conference, Control of Oscillations and Chaos Proceedings. Vol. 2. 27-29 Aug. 1997, St. Peterburg, Russia. New York: IEEE; 1997. P. 207–210. DOI: 10.1109/COC.1997.631327.
  11. Dmitriev AS, Kyarginsky BY, Panas AI, Starkov SO. Experiments on ultra wideband direct chaotic information transmission in microwave band. Int. J. Bifurcat. Chaos. 2003;13(6):1495–1507. DOI: 10.1142/S0218127403007345.
  12. Koronovskii AA, Moskalenko OI, Popov PV, Hramov AE. Method for secure data transmission based on generalized synchronization. Bulletin of the Russian Academy of Sciences: Physics. 2008;72(1):131–135. DOI: 10.1007/s11954-008-1030-7..
  13. Koronovskiy AA, Moskalenko OI, Popov PV, Khramov AE. Method of secret transmission of information. Patent for Invention No. 2295835. Moscow: FIIP; 2007 (in Russian).
  14. Anishchenko VS, Pavlov AN, Janson NB. Global reconstruction in the presence of a priori information. Chaos, Solitons and Fractals. 1998;9(8):1267–1278. DOI: 10.1016/S0960-0779(98)00061-7.
  15. Janson NB, Pavlov AN, Anishchenko VS. Global reconstruction: application to biological data and secure communication. In: Gouesbet G, Meunier-Guttin-Cluzel S, editors. Chaos and its reconstruction. New York: Novascience Publishers; 2003. P. 287–317.
  16. Anishchenko VS, Pavlov AN. Global reconstruction in application to multichannel communication. Phys. Rev. E. 1998;57(2):2455–2457. DOI: 10.1103/PhysRevE.57.2455.
  17. Anishchenko VS, Pavlov AN, Yanson NB. Reconstruction of dynamic systems as applied to secure communications. Tech. Phys. 1998;43(12):1401–1407. DOI: 10.1134/1.1259214.
  18. Gribkov DA, Gribkova VV, Kuznetsov YI, Rzhanov AG. Global dynamical modeling of time series and application to restoration of broadband signal characteristics. AIP Conference Proceedings. 1996;375(1):181–188. DOI: 10.1063/1.51028.
  19. Gribkov DA, Gribkova VV, Kuznetsov YI. Reconstruction of the external influence from the implementation of one variable of the autostochastic system. Moscow University Physics Bulletin. 1995;36(1):76–78 (in Russian).
  20. Bezruchko BP, Smirnov DA. Constructing nonautonomous differential equations from experimental time series. Phys. Rev. E. 2001;63(1):016207. DOI: 10.1103/PhysRevE.63.016207.
  21. Bezruchko BP, Dikanev TV, Smirnov DA. Role of transient processes for reconstruction of model equations from time series. Phys. Rev. E. 2001;64(3):036210. DOI: 10.1103/physreve.64.036210.
  22. Smirnov DA, Sysoev IV, Seleznev EP, Bezruchko BP. Reconstructing nonautonomous system models with discrete spectrum of external action. Tech. Phys. Lett. 2003;29(10):824–827. DOI: 10.1134/1.1623857.
  23. Anishchenko VS, Astakhov VV, Neiman AB, Vadivasova TE, and Schimansky-Geier L. Nonlinear Dynamics of Chaotic and Stochastic Systems. Tutorial and Modern Development. Berlin, Heidelberg: Springer; 2007. 446 p. DOI: 10.1007/978-3-540-38168-6.
  24. Astaf’eva NM. Wavelet analysis: basic theory and some applications. Phys. Usp. 1996;39(11):1085–1108. DOI: 10.1070/PU1996v039n11ABEH000177.
  25. Daubechies I. Ten Lectures on Wavelets. Philadelphie: S.I.A.M.; 1992. 350 p. DOI: 10.1137/1.9781611970104.
  26. Meyer Y. Wavelets: Algorithms and Applications. Philadelphie: S.I.A.M.; 1993. 133 p.
  27. Dremin IM, Ivanov OV, Nechitailo VA. Wavelets and their uses. Phys. Usp. 2001;44(5):447–478. DOI: 10.1070/PU2001v044n05ABEH000918.
Received: 
13.03.2008
Accepted: 
13.03.2008
Published: 
27.02.2009
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