Advertisement

Automatic Detection and Suppression of Parasitic Chirp Signals in the Intermediate Time–Frequency Domain

  • P. E. GolubtsovEmail author
  • I. I. Morozov
Article
  • 15 Downloads

Abstract

The problem of automatic parasitic chirp components detection and suppression in a digital signal is considered. The detection is based on the calculation of the discrete Wigner distribution accompanied by the Hough transform. The filtration is achieved by a series of discrete fractional Fourier transforms converting the signal to special coordinates, where the entire energy of the parasitic signals is accumulated at a few samples and then reset. The main novelty is the utilization of new construction of discrete fractional Fourier transform coordinated with the discrete Wigner distribution. The advantages of the proposed approach are illustrated by the simulations.

Keywords

Chirp signal Fractional Fourier transform Wigner distribution Hough transform 

Notes

References

  1. 1.
    T. Alieva, V. Lopez, F. Agullo-Lopez, L.B. Almeida, The fractional Fourier transform in optical propagation problems. J. Mod. Opt. 41, 1037–1044 (1994)CrossRefGoogle Scholar
  2. 2.
    O.A. Alkishriwo, L.F. Chaparro, A. Akan, Signal separation in the Wigner distribution domain using fractional Fourier transform, in Proceedings of the 19th European Signal Processing Conference (2011), pp. 1879–1883Google Scholar
  3. 3.
    S. Barbarossa, Analysis of multicomponent LFM signals by a combined Wigner-Hough transform. IEEE Trans. Signal Process. 43(6), 1511–1515 (1995)CrossRefGoogle Scholar
  4. 4.
    Ç. Candan, On higher order approximations for Hermite-Gaussian functions and discrete fractional Fourier transforms. IEEE Signal Process. Lett. 14(10), 699–702 (2007)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ç. Candan, M.A. Kutay, H.M. Ozaktas, The discrete fractional Fourier transform. IEEE Trans. Signal Process. 48(5), 1329–1337 (2000)MathSciNetCrossRefGoogle Scholar
  6. 6.
    D.S.K. Chan, A non-aliased discrete-time Wigner distribution for time-frequency signal analysis, in IEEE International Conference on Acoustics, Speech, and Signal Processing, Paris (1982), pp. 1333–1336Google Scholar
  7. 7.
    T.A.C.M. Claasen, W.F.G. Mecklenbräuker, The Wigner distribution: a tool for time-frequency signal analysis; part II: discrete time signals. Philips J. Res. 35, 276–300 (1980)MathSciNetzbMATHGoogle Scholar
  8. 8.
    B.W. Dickinson, K. Steiglitz, Eigenvectors and functions of the discrete Fourier transform. IEEE Trans. Acoust. Speech Signal Process. 30, 25–31 (1982)MathSciNetCrossRefGoogle Scholar
  9. 9.
    R.G. Dorsch, A.W. Lohmann, Y. Bitran, D. Mendlovic, H.M. Ozaktas, Chirp filtering in the fractional Fourier domain. Appl. Opt. 33(32), 7599–7602 (1994)CrossRefGoogle Scholar
  10. 10.
    D. Dragoman, Applications of the Wigner distribution function in signal processing. EURASIP J. Appl. Signal Process. 2005(10), 1520–1534 (2005)zbMATHGoogle Scholar
  11. 11.
    R.O. Duda, P.E. Hart, Use of the Hough transformation to detect lines and curves in pictures. Commun. ACM 15(1), 11–15 (1972)CrossRefGoogle Scholar
  12. 12.
    A.Y. Erdogan et al., FMCW signal detection and parameter extraction by cross Wigner-Hough transform. IEEE Trans. Aerosp. Electron. Syst. 53(1), 334–344 (2017)CrossRefGoogle Scholar
  13. 13.
    F.A. Grunbaum, The eigenvectors of the discrete Fourier transform: a version of the Hermite functions. J. Math. Anal. Appl. 88, 355–363 (1982)MathSciNetCrossRefGoogle Scholar
  14. 14.
    M.T. Hanna, N.P. Seif, W.A.E.M. Ahmed, Discrete fractional Fourier transform based on the eigenvectors of tridiagonal and nearly tridiagonal matrices. Dig. Signal Process. 18(5), 709–727 (2008)CrossRefGoogle Scholar
  15. 15.
    C. Levy, M. Pinchas, Y. Pinhasi, A new approach for the characterization of nonstationary oscillators using the Wigner–Ville distribution. Math. Probl. Eng. (2018).  https://doi.org/10.1155/2018/4942938 MathSciNetCrossRefGoogle Scholar
  16. 16.
    V. Namias, The fractional order Fourier transform and its application to quantum mechanics. J. Inst. Appl. Math. 25, 241–265 (1980)MathSciNetCrossRefGoogle Scholar
  17. 17.
    H.M. Ozaktas, O. Arikan, M.A. Kutay, G.B. Bozdagi, Digital computation of fractional Fourier-transform. IEEE Trans. Signal Process. 44, 2141–2150 (1996)CrossRefGoogle Scholar
  18. 18.
    H.M. Ozaktas, Z. Zalevski, M.A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, New York, 2001)Google Scholar
  19. 19.
    F. Peyrin, R. Prost, A unified definition for the discrete-time, discrete-frequency, and discrete-time/frequency Wigner distributions. IEEE Trans. Acoust. Speech Signal Process. 34(4), 858–867 (1986)CrossRefGoogle Scholar
  20. 20.
    A. Serbes, L. Durak-Ata, The discrete fractional Fourier transform based on the DFT matrix. Signal Process. 91, 571–581 (2011)CrossRefGoogle Scholar
  21. 21.
    R. Torres, E. Torres, Fractional Fourier analysis of random signals and the notion of α-stationarity of the Wigner–Ville distribution. IEEE Trans. Signal Process. 61, 1555–1560 (2013)MathSciNetCrossRefGoogle Scholar
  22. 22.
    E. Wigner, On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759 (1932)CrossRefGoogle Scholar
  23. 23.
    Z. Yin, W. Chen, A new LFM-signal detector based on fractional Fourier transform. EURASIP J. Adv. Signal Process. 1, 876282 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.JSC Radio Engineering Corporation “Vega”MoscowRussian Federation

Personalised recommendations