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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
Chapter
  • 12 Downloads
Part of the Intelligent Systems Reference Library book series (ISRL, volume 184)

Abstract

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.

Keywords

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

Notes

Acknowledgements

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

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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

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