DOI: 10.17586/2226-1494-2018-18-5-905-909


E. S. Ilina, S. V. Bystrov, A. A. Blinnikov

Read the full article 
Article in Russian

For citation: Ilina Е.S., Bystrov S.V., Blinnikov А.А. Frequency determination of pulse signal with constant beat by dint of recurrent usage of Fourier transform. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2018, vol. 18, no. 5, pp. 905–909 (in Russian). doi: 10.17586/2226-1494-2018-18-5-905-909


The paper proposes an algorithm for frequency estimation of a pulse signal with constant beat under significant distortion conditions with the use of spectral analysis methods. The sequential processing of the signal based on the recurrent usage of discrete Fourier transform is shown. The initial pulse signal is represented as a fragment of the Dirac comb. Its Fourier spectrum also contains a fragment of the Dirac comb. To reduce the effect of leakage due to the application of Fourier transform to the finite sequence, a convolution of the signal with a weight window is used. To increase the signal-to-noise ratio and reduce the side lobe level, the spectrum of the initial signal is taken as the original for Fourier transform with an increased number of spectral lines. The necessity of recurrent transformation usage is brought about by the noise of the initial signal and the resulting spectrum after the first application of Fourier transform. In comparison with a single application of the transformation, this approach provides an opportunity to recognize a useful signal both against the background of Gaussian and aperiodic impulse noise, and against the background of signals containing such noise in the Fourier spectrum. We give a method for checking the local maxima of the amplitudes of the obtained discrete Fourier transform for periodicity. The frequency of a pulse signal with constant beat is determined by the element index with the largest number of fulfillment of the periodicity condition.

Keywords: Fourier transform recurrent usage, delta function, Fourier transform, Dirac comb, spectral analysis, noisy signal, leakage effect, Fourier spectrum, window function, digital signal processing

  1. Glebova Е.S., Blinnikov А.А. Modification of steel ladles labels in the problem of automation of the ladles turnover. Journal of Instrument Engineering, 2015, vol. 58, no. 9, pp. 765–769. (in Russian) doi: 10.17586/0021-3454-2015-58-9-765-769
  2. Il'ina E.S., Bystrov S.V. Determining the frequency of a signal with a constant tact in the image. Proc. Congress of Young Scientists. 2017. Available at: (accessed 10.06.2018).
  3. Davydov A.V. Digital Signal Processing. Thematic Lectures. Ekaterinburg, 2005. (in Russian)
  4. Voskoboinikov Yu.E., Gochakov A.V., Kolker A.B. Signals and Images Filtering: Fourier and Wavelet Algorithms (with Examples in Mathcad). Novosibirsk, NSAU Publ., 2010, 188 p. (in Russian)
  5. Smirnov S.A. Transformations of Optical Signals. St. Petersburg, SPbSU ITMO Publ., 2008, 113 p. (in Russian)
  6. Ponomarev Yu.V. Introduction to Spectral, Correlation and Wavelet Analysis. Moscow, MSU Publ., 2012, 284 p. (in Russian)
  7. Gonzales R.C.,Woods R.E. Digital Image Processing. 2nd ed. Upper Saddle River, Prentice Hall, 2002, 793 p.
  8. Kotel’nikov V.A. On the transmission capacity of ’ether’ and wire in electric communications. Physics Uspekhi, 2006, vol. 49, pp. 736–744. doi: 10.1070/PU2006v049n07ABEH006160
  9. Il'ina E.S., Bystrov S.V. Methods for digital image processing to minimize the effect of leakage. Proc. Congress of Young Scientists. 2018. Available at: (accessed 10.06.2018).
  10. Lyons R.G. Understandin Digital Signal Processing. Prentice Hall, 2004.
  11. Khovanova N.A., Khovanov I.A. Time Series Analysis Methods. Saratov, GosUNTs Kolledzh Publ., 2001, 119 p. (in Russian)
  12. Spectral Analysis on a Limited Time Interval. Window Functions. Available at: (accessed 31.05.2018).

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2019 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.