Abstract
The main physical applications of atomic, WA-systems, and R-functions are presented. The Whittaker-Kotelnikov-Shannon sampling theorem is generalized on the basis of atomic functions. Applications of atomic functions in the theory of probability and random processes, interpolation of stationary random processes with atomic functions, and a new class of probabilistic weighting functions used in digital signal and image processing are considered.
Similar content being viewed by others
References
V. L. Rvachev, Geometric Applications of Boolean Algebra (Tekhnika, Kiev, 1967) [in Russian].
V. L. Rvachev, Methods of Boolean Algebra in Mathematical Physics (Naukova Dumka, Kiev, 1974) [in Russian].
V. L. Rvachev, Theory of R-functions and Its Some Applications (Naukova Dumka, Kiev, 1982) [in Russian].
V. L. Rvachev and V. A. Rvachev, Nonclassical Methods of the Approximation Theory in Boundary Value Problems (Naukova Dumka, Kiev, 1979) [in Russian].
V. F. Kravchenko, Lectures on the Theory of Atomic Functions and Their Some Applications (Radiotekhnika, Moscow, 2003) [in Russian].
V. F. Kravchenko and M. A. Basarab, Boolean Algebra and Methods of Approximation in the Boundary Value Problems of Electromagnetics, Ed. by V.F. Kravchenko (Fizmatlit, Moscow, 2004) [in Russian].
E. G. Zelkin, V. F. Kravchenko, and V. I. Gusevskii, Approximation Design Methods in the Antenna Theory (Sains-Press, Moscow, 2005).
V. F. Kravchenko and V. L. Rvachev, Boolean Algebra, Atomic Functions and Wavelets in Physical Applications (Fizmatlit, Moscow, 2006) [in Russian].
Digital Signal and Image Processing in Radiophysical Applications, Ed. by V. F. Kravchenko (Fizmatlit, Moscow, 2007) [in Russian].
V. K. Volosyuk and V. F. Kravchenko, Statistical Theory of Radiotechnical Systems of Remote Sensing and Radar, Ed. by V.F. Kravchenko (Fizmatlit, Moscow, 2008) [in Russian].
V. F. Kravchenko, H. M. Perez-Meana, and V. I. Ponomaryov, Adaptive Digital Processing of Multidimentional Signals with Applications (Fizmatlit, Moscow, 2009).
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].
O. V. Lazorenko and L. F. Chernogor, Ultrawideband Signals and Processes (V.N. Karazin Kharkov: Nats. Univ., Kharkov, 2009) [in Russian].
V. F. Kravchenko, O. V. Kravchenko, V. I. Pustovoit, and D. V. Churikov, Fiz. Osn. Priborostroen., Spec. Iss. p. 3 (2011).
V. K. Volosyuk, Yu. V. Gulyaev, V. F. Kravchenko, B. G. Kutuza, V. V. Pavlikov, and V. I. Pustovoit, J. Commun. Technol. Electron. 59, p. 97 (2014).
V. F. Kravchenko, in Radar and Radio Communication (Proc. 16th Int. Conf., Firsanovka, Moscow Reg., Nov. 11–16, 2008) (MEI, Moscow, 2008), p. 463.
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 (A.S. Popov RNTORES, Moscow, 2012), pp. III–VIII.
V. F. Kravchenko, in Radiation and Scattering of Electromagnetic Waves (Proc. Int. Sci. Conf., Taganrog, Russia, 27 June–1 July, 2009 (Yuzhn. Federal. Univ., Taganrog, 2009), p. 24.
V. F. Kravchenko, in Proc. Int. Conf. on Antenna Theory and Techniques, Lviv, Oct. 6–9, 2009 (Lviv. Politechnic Nat. Univ., Lviv, 2009), p. 3.
V. A. Rvachev, Usp. Mat. Nauk 45, 77 (1990).
V. M. Kolodyazhnyi and V. A. Rvachev, Kibern. Sistemn. Anal., No. 6, p. 155 (2007).
V. F. Kravchenko and A. R. Safin, Elektromagn. Volny Elektron. Sist. 13(12), p. 31 (2008).
V. F. Kravchenko and A. V. Yurin, J. Commun. Technol. Electron. 58, p. 945 (2013).
V. F. Kravchenko, V. I. Pustovoit, and D. V. Churikov, J. Commun. Technol. Electron. 57, 1050 (2012).
V. F. Kravchenko and D. V. Churikov, in Proc. Progress in Electromagnetics Research Symp. (PIERS 2009), Moscow, Aug. 18–21, 2009 (The Electromagnetics Academy, Cambridge, USA, 2009), p. 241.
O. V. Kravchenko and A. R. Safin, in Proc. Progress in Electromagnetics Research Symp. (PIERS 2009), Moscow, Aug. 18–21, 2009 (The Electromagnetics Academy, Cambridge (USA), 2009), p. 249.
V. F. Kravchenko, O. V. Kravchenko, A. R. Safin, in Proc. 2010 Int. Symp. on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves (MSMW), Kharkov, Jun. 21–26, 2010 (IEEE, New York, 2010), MSMW.2010.5546004.
V. F. Kravchenko and D. V. Churikov, in Proc. Int. Conf. “Days on Diffraction (DD-2012)”, St. Petersburg, May 28–June 1, 2012 (IEEE, New York, 2012), p. 158.
V. F. Kravchenko and A. V. Yurin, Am. Inst. Phys. Conf. Proc. 1106, 18 (2009).
V. F. Kravchenko, O. V. Kravchenko, and A. R. Safin, in Proc. Int. Conf. “Days on Diffraction (DD-2009)”, St. Petersburg, May 26–29, 2009 (IEEE, New York, 2009), p. 26.
V. F. Kravchenko, O. V. Kravchenko, and A. R. Safin, Usp. Sovremen. Radioelektron., No. 5, p. 23 (2009).
V. F. Kravchenko, O. V. Kravchenko, A. R. Safin, and D. V. Churikov, Elektromagn. Volny Elektron. Sist. 14(9), p. 31 (2009).
V. F. Kravchenko and D. V. Churikov, J. Meas. Sci. Instrum. 4(3), p. 231 (2013).
V. F. Kravchenko, V. I. Pustovoit, and D. V. Churikov, Dokl. Phys. 56, p. 471 (2011).
V. F. Kravchenko, V. I. Pustovoit, and D. V. Churikov, Elektromagn. Volny Elektron. Sist. 16(8), 44 (2011).
V. F. Kravchenko and D. V. Churikov, in Proc. Int. Conf. “Days on Diffraction (DD-2012)”, St. Petersburg, May 28–June 1, 2012 (IEEE, New York, 2012), p. 152.
V. F. Kravchenko, Ya. Yu. Konovalov, and D. V. Churikov, in Proc. Progress in Electromagnetics Research Symp. (PIERS 2012), Moscow, Aug. 19–23, 2012. (Electromagnetics Academy, Cambridge (USA), 2012), p. 45.
V. F. Kravchenko, O. V. Kravchenko, and A. R. Safin, in Proc. Progress in Electromagnetics Research Symp. (PIERS 2009), Moscow, Aug. 18–21, 2009 (Electromagnetics Academy, Cambridge, USA, 2009), p. 237.
V. F. Kravchenko, O. V. Kravchenko, and A. R. Safin, in Proc. Int. Conf. on Antenna Theory and Techniques, Lviv, Oct. 6–9, 2009 (Lviv. Politechnic Nat. Univ., Lviv, 2009), p. 66.
V. F. Kravchenko and D. V. Churikov, in Proc. Int. Conf. “Days on Diffraction (DD-2011)”, St. Petersburg, May 30–June 3, 2011 (IEEE, New York, 2011), p. 78.
Q. Jiang and S. L. Lee, Adv. Comput. Math. 7, p. 383 (1997).
J. Shen, Methods Appl. Anal. 5, 283 (1998).
R.Q. Jia, S. L. Lee, and A. Sharma, Proc. Am. Math. Soc. 126, 729 (1998).
W. C. Lang, Int. J. Math. and Math. Sci. 2004, p. 3435 (2004).
H. Gotovac, V. Cvetkovic, and R. Andricevic, Adv. Water Resour. 32, 885 (2009).
V. A. Kotel’nikov, Collected Works, Vol. 1: Radiophysics, Informatics, Telecommunications (Fizmatlit, Moscow, 2008) [in Russian].
I. S. Ryzhak, Selected Problems of the Circuit Theory and Signal Processing (BLOK-Inform-Ekspress, Moscow, 2003) [in Russian].
A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968; Mir, Moscow, 1971).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.F. Kravchenko, O.V. Kravchenko, V.I. Pustovoit, D.V. Churikov, 2014, published in Radiotekhnika i Elektronika, 2014, Vol. 59, No. 10, pp. 949–978.
Rights and permissions
About this article
Cite this article
Kravchenko, V.F., Kravchenko, O.V., Pustovoit, V.I. et al. Atomic, WA-systems, and R-functions applied in modern radio physics problems: Part I. J. Commun. Technol. Electron. 59, 981–1009 (2014). https://doi.org/10.1134/S1064226914090046
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064226914090046