Skip to main content
SpringerLink
Log in

Atomic and WA-systems and R-functions applied in modern radio physics problems: Part II

  • Review
  • Published:
Journal of Communications Technology and Electronics Aims and scope Submit manuscript

Abstract

The second part of the review is devoted to the application of the WA-system of Kotel’nikov functions in various physical systems. The calculation algorithms based on wavelets are superior to the Fourier transforms owing to the local properties in both spatial and frequency domains, orthogonality, zero moments, and multiscale analysis of the former. The construction of new classes of orthogonal and analytical WA-systems of the Kravchenko functions based on atomic functions is interesting for scientific applications and practice. The efficiency of such an approach is demonstrated using specific physical examples related to the digital processing of signals and images.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. Ya. Novikov, V. Yu. Protasov, and M. A. Skopina, Theory of Splashes (Fizmatlit, Moscow, 2005) [in Russian].

    Google Scholar 

  2. S. G. Mallat, A Wavelet Tour of Signal Processing (Academic, San Diego, 1998; Mir, Moscow, 2005).

    MATH  Google Scholar 

  3. V. F. Kravchenko and V. L. Rvachev, Boolean Algebra, Atomic Functions, and Wavelets in Physical Applications (Fizmatlit, Moscow, 2006) [in Russian].

    Google Scholar 

  4. V. F. Kravchenko, O. S. Labun’ko, A. M. Lerer, and G. P. Sinyavskii, Computing Methods in Modern Radio Physics (Fizmatlit, Moscow, 2009) [in Russian].

    Google Scholar 

  5. M. A. Basarab, V. K. Volosyuk, O. V. Goryachkin, et al., Digital Signal and Image Processing in Radio-Physical Applications, Ed. by V. F. Kravchenko (Fizmatlit, Moscow, 2007) [in Russian].

  6. V. F. Kravchenko, H. M. Perez-Meana, and V. I. Ponomaryov, Adaptive Digital Processing of Multidimentional Signals with Applications (Fizmatlit, Moscow, 2009) [in Russian].

    Google Scholar 

  7. O. V. Lazorenko and L. F. Chernogor, Ultrabroadband Signals and Processes, Karazin Nats. Univ., Kharkov, 2009) [in Russian].

    Google Scholar 

  8. D. V. Kravchenko and D. V. Churikov, Telecommun. Radio Eng. 70, 759–786 (2011).

    Article  Google Scholar 

  9. V. F. Kravchenko, Lectures on the Theory of Atomic Functions and Their Applications (Radiotekhnika, Moscow, 2003) [in Russian].

    MATH  Google Scholar 

  10. V. F. Kravchenko, O. V. Kravchenko, V. I. Pustovoit, and D. V. Churikov, Fiz. Osnovy Priborostr., Special Issue, 3 (2011).

    Google Scholar 

  11. V. F. Kravchenko, in Radar and Radio Communication (Proc. 16th Int. Conf., Firsanovka, Moscow Reg., Nov. 11–16, 2008) (MEI, Moscow, 2008), p. 463.

    Google Scholar 

  12. V. F. Kravchenko, O. V. Kravchenko, V. I. Pustovoit, and D. V. Churikov, in Proc. 67th Sci. Session of the Popov Society Dedicated to the Radio Day, Moscow, May 16–17, 2012 (RNTORES im. A.S. Popova, Moscow, 2012), pp. III–VIII.

    Google Scholar 

  13. V. F. Kravchenko, in Proc. 7th Int. Conf. on Antenna Theory and Techniques, Lviv, Oct. 6–9, 2009 (Lviv. Polytechnik, Lviv, 2009), p. 3.

    Google Scholar 

  14. V. F. Kravchenko, V. L. Rvachev, and V. A. Rvachev, Radiotekh. Elektron. (Moscow) 40, 1385 (1995).

    Google Scholar 

  15. Yu. V. Gulyaev, V. F. Kravchenko, and V. I. Pustovoit, Dokl. Phys. 52, 645 (2007).

    Article  Google Scholar 

  16. Yu. V. Gulyaev, V. F. Kravchenko, and V. I. Pustovoit, Dokl. Math. 75, 325 (2007).

    Article  MathSciNet  Google Scholar 

  17. V. F. Kravchenko and A. V. Yurin, Elektromagn. Volny Elektron. Sist. 13(8), 12 (2008).

    Google Scholar 

  18. V. F. Kravchenko and A. V. Yurin, Usp. Sovremen. Radioelektron., No. 5, 3 (2008).

    Google Scholar 

  19. V. F. Kravchenko and D. V. Churikov, Usp. Sovremen. Radioelektron, No. 6, 67 (2008).

    Google Scholar 

  20. V. F. Kravchenko and D. V. Churikov, Usp. Sovremen. Radioelektron, No. 8, 39 (2008).

    Google Scholar 

  21. V. F. Kravchenko, V. I. Ponomaryov, and J. L. Sanchez-Ramirez, Telecommun. Radio Eng. 87, 853 (2008).

    Article  Google Scholar 

  22. V. F. Kravchenko and D. V. Churikov, in Proc. 4th Int. Conf. on Ultrawideband and Ultrashort Impulse Signals (UWUIS 2008), Sevastopol, Sep. 15–19, 2008 (IEEE, New York, 2008), p. 27.

    Book  Google Scholar 

  23. V. F. Kravchenko and D. V. Churikov, in Proc. Mathematical Modeling of Wave Phenomena Conf. MMWP-08), Vaxjo, Jun. 9–13, 2008 (Vaxjo Univ. Vaxjo, 2008), p. 39.

    Google Scholar 

  24. V. F. Kravchenko and A. V. Yurin, Elektromagn. Volny Elektron. Sist. 14(3), 4 (2009).

    Google Scholar 

  25. V. F. Kravchenko and V. I. Pustovoit, Dokl. Math. 80, 775 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  26. V. F. Kravchenko and D. V. Churikov, Telecommun. Radio Eng. 68, 649 (2009).

    Article  Google Scholar 

  27. F. Gomeztagle, V. F. Kravchenko, and V. I. Ponomaryov, Telecommun. Radio Eng. 68, 747 (2009).

    Article  Google Scholar 

  28. F. Gomeztagle, V. Kravchenko, and V. Ponomaryov, in Proc. 20th Associat. of Sci. and Technolog. Development (IASTED) Int. Conf. on Modelling and Simulation, Banff, July 6–8, 2009 (ACTA, Calgary, 2009), p. 187.

    Google Scholar 

  29. V. Kravchenko, H. P. Meana, V. Ponomaryov, and D. Churikov, in Proc. 14th Iberoamerican Conf. on Pattern Recognition (CIARP2009), Guadalajara, Nov. 15–18, 2009 (Springer-Verlag, Berlin, 2009).

    Google Scholar 

  30. V. F. Kravchenko and A. V. Yurin, in Proc. Progress in Electromagnetics Research Symposium, Moscow, Aug. 18–21, 2009 (Electromagnetics Academy, Cambridge, MA, 2009).

    Google Scholar 

  31. V. F. Kravchenko, C. Juarez-Landin, V. Ponomaryov, J. L. Sanchez-Ramirez, and M. Martinez-Reyes, “Wavelets based on atomic function used in detection and classification of masses in mammography,” (MICAI-2008), Adv. Art. Intell. 5317, 295–304 (2008).

    Google Scholar 

  32. V. F. Kravchenko and A. Y. Koshelev, Telecommun. Radio Eng. 69, 305 (2010).

    Article  Google Scholar 

  33. V. F. Kravchenko, V. I. Ponomaryov, and V. I. Pustovoit, Dokl. Phys. 56, 479 (2011).

    Article  Google Scholar 

  34. V. F. Kravchenko and D. V. Churikov, Elektromagn. Volny Elektron. Sist. 15, 3 (2010).

    Google Scholar 

  35. V. F. Kravchenko and D. V. Churikov, in Proc. Int. Conf. “Days on Diffraction”, St.Petersburg, June 8–11, 2010 (IEEE, New York, 2010), pp. 93–98.

    Google Scholar 

  36. V. F. Kravchenko and D. V. Churikov, in Proc. Int. Conf. “Days on Diffraction”, St.Petersburg, 30 May–3 Jun. 2011 (IEEE, New York, 2011), p. 106.

    Book  Google Scholar 

  37. V. Ponomaryov, F. Gomeztagle, and V. Kravchenko, in Proc. 17th Int. Conf. on Digital Signal Processing (DSP), Corfu, Greece, July 6–8, 2011 (IEEE, New York, 2011), p. ICDSP.2011.6004972.

    Google Scholar 

  38. V. F. Kravchenko, V. I. Pustovoit, and D. V. Churikov, Dokl. Phys. 56, 92 (2011).

    Article  Google Scholar 

  39. V. F. Kravchenko, V. I. Pustovoit, and D. V. Churikov, Dokl. Phys. 56, 373 (2011).

    Article  Google Scholar 

  40. V. L. Rvachev, Theory of R-Functions and Its Applications (Naukova Dumka, Kiev, 1982) [in Russian].

    MATH  Google Scholar 

  41. V. F. Kravchenko, V. I. Pustovoit, and D. V. Churikov, Elektromagn. Volny Elektron. Sist. 16(9), 7 (2011).

    Google Scholar 

  42. V. F. Kravchenko, D. V. Churikov, V. I. Ponomaryov, and H. M. Perez-Meana, in Acoustooptical and Radar Methods of Measurements and Information Processing (Proc. 5nd Int. Conf., Suzdal’, Russia, Sept. 18–19, 2012) (RNTORES im. A. S. Popova, Moscow, 2012), p. 3.

    Google Scholar 

  43. O. V. Kravchenko and D. V. Churikov, in Proc. Progress in Electromagnetics Research Symp. (PIERS 2012), Moscow, Aug. 19–23, 2012 (Electromagn. Academy, Cambridge MA, 2012), p. 1236.

    Google Scholar 

  44. V. F. Kravchenko and D. V. Churikov, J. Meas. Sci. Instrum. 3, 345 (2012).

    Google Scholar 

  45. V. F. Kravchenko, D. V. Churikov, V. I. Ponomaryov, and H. M. Perez-Meana, in Proc. Progress in Electro-magnetics Research Symp. (PIERS 2012), Moscow, Aug. 19–23, 2012 (Electromagn. Academy, Cambridge MA, 2012), p. 40.

    Google Scholar 

  46. H. Chavez-Roman, G. Duchen-Sanchez, V. F. Kravchenko, and V. I. Ponomaryov, Telecommun. Radio Eng. 72, 1803 (2013).

    Article  Google Scholar 

  47. V. F. Kravchenko, V. I. Pustovoit, and D. V. Churikov, Dokl. Phys. 58, 131 (2013).

    Article  Google Scholar 

  48. V. K. Volosyuk, Yu. V. Gulyaev, V. F. Kravchenko, et al., in Proc. Int. Conf. “Digital Signal Processing and Its Application, DSPA-2012”, Moscow, Mar. 27–29, 2013 (RNTORES im. A. S. Popova, Moscow, 2013), p. 3.

    Google Scholar 

  49. V. F. Kravchenko, V. I. Pustovoit, and D. V. Churikov, Dokl. Akad. Nauk 456, 214 (2014).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Mokhovaya ul. 11, korp. 7, Moscow, 125009, Russia

    V. F. Kravchenko, O. V. Kravchenko & D. V. Churikov

  2. Bauman State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005, Russia

    V. F. Kravchenko, O. V. Kravchenko, V. I. Pustovoit & A. V. Yurin

  3. Scientific and Technological Center of Unique Instrumentation, Russian Academy of Sciences, ul. Butlerova 15, Moscow, 117342, Russia

    V. F. Kravchenko, V. I. Pustovoit & D. V. Churikov

  4. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    D. V. Churikov

Authors
  1. V. F. Kravchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. V. Kravchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. I. Pustovoit
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. V. Churikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. V. Yurin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. F. Kravchenko.

Additional information

Original Russian Text © V.F. Kravchenko, O.V. Kravchenko, V.I. Pustovoit, D.V. Churikov, A.V. Yurin, 2015, published in Radiotekhnika i Elektronika, 2015, Vol. 60, No. 2, pp. 109–148.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kravchenko, V.F., Kravchenko, O.V., Pustovoit, V.I. et al. Atomic and WA-systems and R-functions applied in modern radio physics problems: Part II. J. Commun. Technol. Electron. 60, 103–141 (2015). https://doi.org/10.1134/S1064226915020084

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064226915020084

Keywords

Search

Navigation