Sliding Spatial Frequency Processing of Discrete Signals

  • Olga V. Ponomareva
  • Alexey V. PonomarevEmail author
  • Natalya V. Smirnova
Part of the Intelligent Systems Reference Library book series (ISRL, volume 184)


The definition of sliding spatial-frequency processing of discrete signal is given. Fast methods for analyzing two-dimensional discrete signals in the spatial-frequency domain are proposed. The mathematical apparatus of direct two-dimensional discrete Fourier transform in the algebraic and matrix forms is considered. A step by step implementation of two-dimensional discrete Fourier transform based on one-dimensional fast Fourier transform is considered. Effective methods and algorithms for horizontally sliding two-dimensional discrete Fourier transform have been developed that allow us to calculate the coefficients of this transform in time. The developed algorithms efficiency (in terms of computational costs) of real horizontally sliding two-dimensional discrete Fourier transform is evaluated in comparison with the known algorithms. As a result of experimental studies on model two-dimensional discrete signals, the validity, efficiency, and reliability of the proposed methods and algorithms for horizontally sliding two-dimensional discrete Fourier transform have been proved. The relative saving of computations in the developed fast algorithms of horizontal sliding two-dimensional discrete Fourier transform was compared with the standard algorithm.


Sliding spatial frequency processing Discrete two-dimensional signal Two-dimensional discrete Fourier transform Horizontally sliding two-dimensional discrete Fourier transform Spatial-frequency domain Efficiency 


  1. 1.
    Pratt, W.K.: Digital Image Processing. 4th edn. Wiley (2007)Google Scholar
  2. 2.
    Dudgeon, D.E.: Multidimensional Digital Signal Processing. Prentice Hall (1995)Google Scholar
  3. 3.
    Marpl, S.L.: Digital Spectral Analysis: With Applications. Prentice-Hall, New Jersey (1986)Google Scholar
  4. 4.
    Yaroslavsky, L.P.: Compression, restoration, resampling, “compressive sensing”: fast transforms in digital imaging. J. Opt. 17(7), 073001 (2015)CrossRefGoogle Scholar
  5. 5.
    Favorskaya, M.N., Jain, L.C.: Development of mathematical theory in computer vision. In: Favorskay, M.N., Jain, L.C. (eds.) Computer Vision in Control Systems-1: Mathematical Theory, ISRL, vol. 73, pp. 1–8. Springer, Switzerland (2015)CrossRefGoogle Scholar
  6. 6.
    Gonzalez RC, Woods, R.E.: Digital Image Processing. 4th edn. Published by PearsonGoogle Scholar
  7. 7.
    John, W.: Multidimensional Signal, Image, and Video Processing and Coding. Academic Press is imprint of Elsevier (2006)Google Scholar
  8. 8.
    Ponomarev, V.A., Ponomareva, O.V., Ponomarev, A.V.: Method for effective measurement of a sliding parametric Fourier spectrum. Optoelectron. Instrum. Data Process 50(2), 1–7 (2014)CrossRefGoogle Scholar
  9. 9.
    Ponomareva, O., Ponomarev, A., Ponomarev, V.: Evolution of forward and inverse discrete Fourier transform. In: IEEE East-West Design & Test Symposium, pp. 313–318 (2018)Google Scholar
  10. 10.
    Ponomareva, O., Ponomarev, A., Ponomareva, N.: Window-presume parametric discrete Fourier transform. IEEE East-West Design & Test Symposium, pp. 364–368 (2018)Google Scholar
  11. 11.
    Favorskaya, M.N., Buryachenko, V.V., Zotin, A.G., Pahirka, A.I.: Video completion in digital stabilization task using pseudo-panoramic technique. In: The International Archives of Photogrammetry Remote Sensing and Spatial Information Sciences, XLII-2/W4, pp. 83–90 (2017)Google Scholar
  12. 12.
    Favorskaya, M.N., Jain, L.C., Savchina, E.I.: Perceptually tuned watermarking using non-subsampled shearlet transform. In: Favorskay M.N., Jain L.C. (eds.) Computer Vision in Control Systems-3: Aerial and Satellite Image Processing, ISRL, vol. 135, pp. 41–69. Springer (2018)Google Scholar
  13. 13.
    Petrovsky, N.A., Rybenkov, E.V., Petrovsky, A.A.: Two-dimensional non-separable quaternionic paraunitary filter banks. In: IEEE International Conference on Signal Processing: Algorithms, Architectures, Arrangements, and Applications, Poznan, Poland, pp. 120–125 (2018)Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Olga V. Ponomareva
    • 1
  • Alexey V. Ponomarev
    • 1
    Email author
  • Natalya V. Smirnova
    • 1
  1. 1.Kalashnikov Izhevsk State Technical UniversityIzhevsk, Udmurt RepublicRussian Federation

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