The Development of the Algorithm for Estimating the Spectral Correlation Function Based on Two-Dimensional Fast Fourier Transform

  • Timofey ShevgunovEmail author
  • Evgeniy Efimov
  • Vladimir Kirdyashkin
  • Tatiana Kravchenko
Part of the Intelligent Systems Reference Library book series (ISRL, volume 184)


This chapter presents the algorithm for estimating spectral correlation function of a random process that is a valid bi-frequency description of the probabilistic properties of any wide-sense cyclostationary process and relates to its cyclic autocorrelation function via Fourier transform. The key point of the algorithm is that it is based on the two-dimensional discrete Fourier transform of the sample dyadic correlation function weighted by the two-dimensional windowing function, which is rectangular in the direction orthogonal to the current-time axis shape. The dedicated mathematical software libraries implementing fast Fourier transform, which is typically used for image processing, achieve higher performance in comparison with other algorithms involving spectra accumulation. The signal containing a pulse sequence with random amplitudes masked by the additive stationary white Gaussian noise is used in numerical simulation to provide an example of the spectral correlation function estimation procedure and obtain results demonstrating the effectiveness of the proposed algorithm.


Cyclostationarity Cyclic frequency Spectral correlation function Spectral correlation density Fast fourier transform Two-dimensional FFT Pseudo-power 



This work was supported by state assignment of the Ministry of Education and Science of the Russian Federation (project 8.8502.2017/BP).


  1. 1.
    Gardner, W.A.: Cyclostationarity in Communications and Signal Processing. IEEE Press, New York (1994)zbMATHGoogle Scholar
  2. 2.
    Roberts, R.S., Brown, W.A., Loomis, H.H.: Computationally efficient algorithms for cyclic spectral analysis. IEEE Signal Process. Mag. 8(2), 38–49 (1991)CrossRefGoogle Scholar
  3. 3.
    Brown, W.A., Loomis, H.H.: Digital implementations of spectral correlation analyzers. IEEE Trans. Signal Process. 41(2), 703–720 (1993)CrossRefGoogle Scholar
  4. 4.
    Shevgunov, T., Efimov, E., Zhukov, D.: Algorithm 2 N-FFT for estimation cyclic spectral density. Electrosvyaz 2017(6), 50–57 (2017)Google Scholar
  5. 5.
    Shevgunov, T., Efimov, E., Zhukov, D.: Averaged absolute spectral correlation density estimator. In: Moscow Workshop on Electronic and Networking Technologies, pp. 1–4 (2018)Google Scholar
  6. 6.
    Efimov, E., Shevgunov, T., Kuznetsov, Y.: Cyclic spectrum power density estimation of info-communication signals. Trudy MAI 97, 14 (2017)Google Scholar
  7. 7.
    Marple Jr., S.L.: Digital Spectral Analysis: With Applications. Prentice Hall, N.Y. (1987)Google Scholar
  8. 8.
    Gonzalez, R.C., Woods R.E.: Digital Image Processing, 4th edn. Pearson (2018)Google Scholar
  9. 9.
    Kammler, D.W.: A First Course in Fourier Analysis, 2nd edn. Cambridge University Press (2007)Google Scholar
  10. 10.
    Samorodnitsky, G., Taqqu M.S.: Stable Non-gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman and Hall/CRC (1994)Google Scholar
  11. 11.
    Napolitano, A.: Cyclostationary Processes and Time Series: Theory, Applications, and Generalizations. Academic Press (2019)Google Scholar
  12. 12.
    Lighthill M.J.: An Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press (1958)Google Scholar
  13. 13.
    Lenart, L.: Asymptotic distributions and subsampling in spectral analysis for almost periodically correlated time series. Bernoulli 17(1), 290–319 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Shevgunov, T.: A comparative example of cyclostationary description of a non-stationary random process. J. Phys.: Conf. Ser. 1163, 012037 (2019)Google Scholar
  15. 15.
    Efimov, E., Shevgunov, T., Kuznetsov, Y.: Time Delay Estimation of Cyclostationary Signals on PCB Using Spectral Correlation Function, pp. 184–187. Baltic URSI Symposium, Poznan (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Timofey Shevgunov
    • 1
    • 2
    Email author
  • Evgeniy Efimov
    • 1
  • Vladimir Kirdyashkin
    • 1
  • Tatiana Kravchenko
    • 2
  1. 1.Moscow Aviation Institute (National Research University)MoscowRussian Federation
  2. 2.National Research University Higher School of EconomicsMoscowRussian Federation

Personalised recommendations