Skip to main content
SpringerLink
Log in

DFT Spectrum-Sparsity-based Quasi-Periodic Signal Identification and Application

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This study addresses identification of the quasi-periodic sequence based on the discrete Fourier transform spectrum-sparsity. A quasi-periodic signal displays similarities to a periodic signal but does not satisfy its strict definition. Then identification of the quasi-periodic signal is practically a requirement for many applications. The spectrum-sparse property in the Fourier domain is presented for describing the discrete-time periodic signals, and then it is extended and proposed for the quasi-periodic sequence identification. The proposed identification method is applied to real applications including periodicity detection of the sunspot activity, rainfall activity, and air temperature movement as well as the pile driver sound detection. The experimental results and analysis indicate potentiality of the proposed method that it yields satisfying results in the real applications.

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

Access this article

Log in via an institution

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. R.G. Baraniuk, Compressive sensing. IEEE Signal Proc. Mag. 24, 118–124 (2007)

    Article  Google Scholar 

  2. C. Candan, M.A. Kutay, H.M. Ozaktas, The discrete fractional Fourier transform. IEEE Trans. Signal Process. 48, 1329–1337 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. E.J. Candes, J. Romberg, T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52, 489–509 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. E.J. Candes, T. Tao, Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inf. Theory 52, 5406–5423 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. E.J. Candes, W. Michael, An introduction to compressive sampling. IEEE Signal Proc. Mag. 25, 21–30 (2008)

    Article  Google Scholar 

  6. E.J. Candes, Y. Plan, A probabilistic and RIPless theory of compressed sensing. IEEE Trans. Inf. Theory 57, 7235–7254 (2011)

    Article  MathSciNet  Google Scholar 

  7. D. Dohoho, Compressed sensing. IEEE Trans. Inf. Theory 52, 1289–1306 (2006)

    Article  Google Scholar 

  8. P. Duhamel, B. Piron, J.M. Etcheto, On computing the inverse DFT. IEEE Trans. Acoust. Speech Signal Process. 36, 285–286 (1988)

    Article  MATH  Google Scholar 

  9. P. Duhamel, M. Vetterli, Fast Fourier transforms: a tutorial review and a state of the art. Signal Process. 19, 259–299 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  10. S. Gurevich, R. Hadani, N. Sochen, The finite harmonic oscillator and its applications to sequences, communication and radar. IEEE Trans. Inf. Theory 54, 4239–4253 (2008)

    Article  MathSciNet  Google Scholar 

  11. S. Gurevich, R. Hadani, On the diagonalization of the discrete Fourier transform. Appl. Comput. Harmon. Anal. 27, 87–99 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. National Aeronautics and Space Administration (NASA): The Sunspot Cycle. http://solarscience.msfc.nasa.gov/SunspotCycle.shtml. Accessed 1 Jan (2011)

  13. D.J. Nyarko, K.A. Strsmsmoe, in Proceedings of the IEEE on Electrical and Computer Engineering (Calgary, Alta), pp. 708–711 (1996)

  14. A.V. Oppenheim, R.W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, Upper Saddle River, 1989)

    MATH  Google Scholar 

  15. C. Reller, H.-A. Loeliger, J.P.M. Diaz, in 19th European Signal Processing Conference (Barcelona, Spain), pp. 971–975 (2011)

  16. J. Stalker, Complex Analysis: Fundamentals of the Classical Theory of Functions (Springer, Berlin, 1998)

    Book  MATH  Google Scholar 

  17. D. Tominaga, K. Horimoto, Judgment alforithm for periodicity of time series data based on bayesian information criterion. J. Bioinform. Comput. Biol. 6, 747–757 (2008)

    Article  Google Scholar 

  18. D. Tominaga, Periodicity detection method for small-sample time series datasets. Bioinform. Biol. Insights 4, 127–136 (2010)

    Article  Google Scholar 

  19. J.A. Tropp, A.C. Gilbert, Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53, 4655–4666 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. J.G. Vargas-Rubio, B. Santhanam, On the multiangle centered discrete fractional Fourier transform. IEEE Signal Process. Lett. 12, 273–276 (2005)

    Article  Google Scholar 

  21. S. Vaughan, A simple test for periodic signals in red noise. Astron. Astrophys. 431, 391–403 (2005)

    Article  Google Scholar 

  22. Z.C. Yang, A study on the orbit of air temperature movement. Environ. Model. Assess. 12, 131–143 (2007)

    Article  Google Scholar 

  23. P. Zubrycki, A. Petrovsky, in IEEE Proceedings on Circuits and Systems (France, Paris), pp. 2374–2377 (2010)

Download references

Acknowledgments

The research was supported by Scientific Research Fund of Hunan Provincial Science and Technology Department (2013GK3090) and Research Fund of Hunan University of Science and Technology (E50811).

Author information

Authors and Affiliations

  1. School of Information and Electronical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, China

    Zong-chang Yang

Authors
  1. Zong-chang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zong-chang Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, Zc. DFT Spectrum-Sparsity-based Quasi-Periodic Signal Identification and Application. Circuits Syst Signal Process 34, 3543–3557 (2015). https://doi.org/10.1007/s00034-015-0022-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-015-0022-8

Keywords

Search

Navigation