Skip to main content

Advertisement

Springer Nature Link
Log in

On the correlation of chaotic signals generated by multimodal skew tent map

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In recent years, a great deal of attention has been devoted to the application of chaos theory in signal processing and communications. Despite the importance of spectral analysis in these domains, there are few works that take an interest in spectral properties of chaotic signals. In this work, we derive analytic expressions for the autocorrelation function and the auto-spectral density function of chaotic signals generated by a multimodal skew tent map. Our results reveal that chaotic signals generated from a multimodal skew tent map have similar spectral properties to those generated from a unimodal skew tent map.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Lau, F.C.M., Tse, C.K., Ye, M., Hau, S.F.: Coexistence of chaos-based and conventional digital communication systems of equal bit rate. IEEE Trans. Circuits Syst. I Regul. Pap. 51(2), 391–408 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chrysochos, E., Fotopoulos, V., Xenos, M., Skodras, A.N.: Hybrid watermarking based on chaos and histogram modification. Signal Image Video Process. 8, 843–857 (2014)

    Article  Google Scholar 

  3. Caragata, D., Tutanescu, I.: On the security of a new image encryption scheme based on a chaotic function. Signal Image Video Process. 8(4), 641–646 (2014)

    Article  Google Scholar 

  4. Akbil, B., Ferre, G., Aboutajdine, D.: Computational complexity and bandwidth resource analysis of NLM interleaver in IDMA system. In: Image Processing and Communications Challenges 4, AISC, vol. 184, pp 241–251 (2013)

  5. Escribano, F.J., Wagemakers, A., Sanjuán, M.A.F.: Chaos-based turbo systems in fading channels. IEEE Trans. Circuits Syst. I Regul. Pap. 61(2), 530–541 (2014)

    Article  Google Scholar 

  6. Sakai, H., Tokumaru, H.: Autocorrelation of a certain chaos. IEEE Trans. Acoust. Speech Signal Process. 28(5), 588–590 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  7. Talwalkar, S.A., Kay, S.M.: Realization of correlated chaotic signals. In: Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, pp. 1360–1363. Detroit, May 9–12 (1995)

  8. Eisencraft, M., Kato, D.M., Monteiro, L.H.A.: Spectral properties of chaotic signals generated by the skew tent map. Signal Process. 90(1), 385–390 (2010)

    Article  MATH  Google Scholar 

  9. Feltekh, K., Fournier-Prunaret, D., Belghith, S.: Analytical expressions for power spectral density issued from one-dimensional continuous piecewise linear maps with three slopes. Signal Process. 94, 149–157 (2014)

    Article  Google Scholar 

  10. da Costa, R.A., Loiola, M.B., Eisencraft, M.: Correlation and spectral properties of chaotic signals generated by a piecewise-linear map with multiple segments. Signal Process. 133, 187–191 (2017)

    Article  Google Scholar 

  11. Campos-Cantón, E., Femat, R., Pisarchik, A.N.: A family of multimodal dynamic maps. Commun. Nonlinear Sci. Numer. Simul. 16, 3457–3462 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lasota, A., Mackey, M.C.: Chaos, Fractals, and Noise Stochastic Aspects of Dynamics. Springer, Berlin (1994)

    Book  MATH  Google Scholar 

  13. Boyarsky, A., Göra, P.: Laws of Chaos Invariant Measures and Dynamical Systems in One Dimension. Springer, Berlin (1997)

    MATH  Google Scholar 

  14. Lasota, A., Mackey, M.C.: Probabilistic Properties of Deterministic Systems. Cambridge University Press, Cambridge (1985)

    Book  MATH  Google Scholar 

  15. Wolf, A.: Quantifying chaos with Lyapunov exponents. In: Holden, A.V. (ed.) Chaos, pp. 270–290. Princeton University Press, New Jersey (1986)

    Google Scholar 

Download references

Acknowledgements

The authors wish express their sincere thanks to all who helped improving the quality of this paper.

Author information

Authors and Affiliations

  1. Signal and Communications Laboratory, Ecole Nationale Polytechnique, 10, Av. Hassen Badi, P.O. Box 182, 16200, El-Harrach, Algeria

    Ahmed Sahnoune & Daoud Berkani

Authors
  1. Ahmed Sahnoune
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Daoud Berkani
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Ahmed Sahnoune.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sahnoune, A., Berkani, D. On the correlation of chaotic signals generated by multimodal skew tent map. SIViP 12, 1273–1278 (2018). https://doi.org/10.1007/s11760-018-1279-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-018-1279-8

Keywords