TELECOMMUNICATIONS AND RADIO ENGINEERING - 2011 Vol. 70,
No 4 		 

 

 

 

ANALYTICAL DESCRIPTION OF COMPLEX SHAPE LOCUS WITH THE HELP OF R-OPERATIONS AND ATOMIC FUNCTIONS. THE DIGITAL SIGNAL AND IMAGE PROCESSING


V.F. Kravchenko1, D.V. Churikov1, & A.V. Yurin2
1Kotel’nikov Institute of Radio Engineering and Electronics of RAS,
Moscow, Russia
2Bauman Moscow State Technical University, Moscow, Russia
Address all correspondence to V.F. Kravchenko E-mail: olegk@lianet.ru

Abstract
The first part of the article is devoted to the theory of R-functions which is based on the methods of Boolean algebra and atomic functions with reference to the description of complex shape locus. The second part is dedicated to the construction of 2D Kravchenko weight functions (windows) on the basis of irregular shape areas for digital multidimensional signal and image processing.
KEY WORDS:atomic function, R-function, weight function, signal processing

References

  1. Kravchenko, V.F. and Rvachev, V.L., (2006), Boolean algebra, atomic functions and wavelets in physical applications. Fizmatlit, Moscow (in Russian).
  2. Rvachev, V.L., (1982), The theory of R-functions and some applications of them. Naukova dumka, Kiev (in Russian).
  3. Kravchenko, V.F., (ed.) (2007), Digital Signal and Image Processing in Radio Physical Applications. Fizmatlit, Moscow (in Russian).
  4. Kravchenko, V.F., (2003), Lectures on the theory of atomic functions and their some applications. Radio Engineering, Moscow (in Russian).
  5. Kravchenko, V.F., Perez-Meana, H.M., and Ponomaryov, V.I., (2009), Adaptive Digital Processing of Multidimentional Signals with Applications. Fizmatlit, Moscow (in Russian).
  6. Kravchenko V.F. and Basarab M.A., (2004), Boolean algebra and approximation methods in boundary value problems of electrodynamics. Fizmatlit, Moscow (in Russian).
  7. Zelkin, E.G., Kravchenko, V.F., and Gusevskiy, V.I., (2005), Constructive methods of approximation in the theory of antennas. Science-Press, Moscow (in Russian).
  8. Kravchenko, V.F., (2006), Electrodynamics of superconducting structures. Theory, algorithms and computing methods. Fizmatlit, Moscow (in Russian).
  9. Basarab, M.A., Kravchenko, V.F., and Matveev, V.A., (2005), Mathematical modeling of the physical processes in gyroscoping. Radio Engineering, Moscow (in Russian).
  10. Sologub, A.V., Anshakov, E.P., and Danilov, V.V., (1993), Spacecrafts of the remote sensing systems of the Earth’s surface. The mathematical models increasing the effectiveness of  spacecrafts. Mashinostroenie, Moscow (in Russian).
  11. Goncharenko, A.A., Kravchenko, V.F., and Ponomarev, V.I., (1991), Remote sensing of inhomogeneous mediums. Mashinostroenie, Moscow (in Russian).
  12. Nebabin, V.G. and Sergeev, V.V., (1984), Methods and technical devices of radar determination. Radio and Communication, Moscow (in Russian).
  13. Sokolov, A.V., (ed.) (2007), Detecting and identification of radiolocation objects. Radio Engineering, Moscow (in Russian).
  14. Shtager, E.A., (1986), Radio scattering over the complex shape objects. Radio and Communication, Moscow (in Russian).
  15. Vasilenko, G.I. and Taratorin, A.M., (1986), Images reconstruction. Radio and Communication, Moscow (in Russian).
  16. Gonsales, R. and Wuds, R., (2005), Digital image processing. Technosphera, Moscow (in Russian).
  17. Hern, D. and Beyker, M P., (2005), Computer graphics and OpenGL standard. Publishing House “Williams”, Moscow (in Russian).
  18. Dadgion, D. and Mersere, R., (1988), Digital processing of multidimensional signals. Mir, Moscow (in Russian).
  19. Furman, Ya.A., (2003), The introduction into contour analysis. Fizmatlit, Moscow (in Russian).
  20. Tatarenko N.I and Kravchenko V.F., (2006), The field-emission nanostructures and the devices base on them. Fizmatlit, Moscow (in Russian).
  21. Malcev, P.P., (ed.) (2005), Nano- and Microsystem engineering. From investigations up the engineering. Technosphera, Moscow (in Russian).
  22. Haykin, S., (2006), Neural networks: the full course. Publishing House “Williams”, Moscow (in Russian).
  23. Sklyar, B., (2003), Digital communication. Theoretical basis and practical application. Publishing House “Williams”, Moscow (in Russian).
  24. Yacenkov, V.S., (2005), The foundations of satellite navigation. GPS NAVSTAR and GLONASS systems. Hot line – Telecom, Moscow (in Russian).
  25. Anderson, J.A., (2003), Discrete mathematics and combinatorics. Publishing House “Williams”, Moscow (in Russian).
  26. Shirman, Ya.D., (ed.) (2007), Radioelectronic systems: theory and basis of constructing. Radio Engineering, Moscow (in Russian).
  27. Kravchenko, V.F., (2009), Atomic and R-functions in Radiophysical Applications. Review. Proc. International Conference on Antenna Theory and Techniques, 6-9 October, 2009, Lviv, Ukraine.
  28. Kravchenko, V.F. and Yurin, A.V., (2009), The Application of R-Functions Theory and Wavelets to the Boundary Value Problems Solving of the Elliptic Type. International Journal Electromagnetic Waves and Electronic Systems, Moscow, 14(3): 4-39.
  29. Kravchenko, V.F. and Churikov, D.V., (2009), Synthesis of Two-Dimensional Digital Filters with Non Standard Geometry of Supports. Successes of Modern Radio Electronics, 5:3-12 (in Russian).
  30. Kravchenko, V.F., Fedorov, I.B., and Churikov, D.V., (2005), V.L. Rvachov functions and atomic functions in the description problems of the compound contour objects and in digital image processing. Electromagnetic Waves and Electronic Systems, Moscow, 10(7):70-80.


pages 283-323

Back