Atomic and R-functions in radiophysical applications
DOI:
https://doi.org/10.1109/ICATT.2009.4435101Keywords:
atomic and R-functions, synthesis and analysis, WA-system functionsAbstract
This review consist of two parts. First part of review concerned with atomic functions theory and it’s applications in digital signal processing problems, antennas synthesis and sampling theorem. In second part R-functions theory and WA-system functions are considered in applications to boundary-value problems of elliptic type.References
RVACHOV, V.L.; RVACHEV, V.A. On one compactly supported function. Dokl. Akad. Nauk Ukr. SSR, Ser. A, 1971, p.705-707.
RVACHOV, V.L.; RVACHEV, V.A. Atomic functions in mathematical physics’ published in the book Mathematization of Knowledge and Scientific-Engineering Progress. Kiev: Naukova Dumka, 1975, p.188-199.
RVACHOV, V.L.; RVACHEV, V.A. Nonclassical Methods of Approximation Theory in Boundary-Value problems. Kiev: Naukova Dumka, 1979.
RVACHEV, V.L. The R-function Theory and Its Some Applications. Kiev: Naukova Dumka, 1982.
KRAVCHENKO, V.F. Lectures on the Theory of Atomic Functions and Their Some Applications. Moscow: Radiotechnika, 2003.
KRAVCHENKO, V.F.; RVACHEV, V.L. Algebra of Logic, Atomic Functions, and Wavelets in Physical Applications. Moscow: Fizmatlit, 2006.
KRAVCHENKO, V.F. (ed.) Digital Signal and Image Processing in Radio Physical Applications. Moscow: Fizmatlit, 2007 [in Russian].
KRAVCHENKO, V.F.; YURIN, A.V. The Selection of Basis Functions Systems for Determination of Cutoff Frequency of Waveguides and Resonators of Complex Shape with the Help of R-functions Method. Mathematical Modeling of Wave Phenomena, Proc. of 3rd Conf. on Mathematical Modeling of Wave Phenomena and 20th Nordic Conference on Radio Science and Communications, Växjö, Sweden, June 9-13, 2008. American Institute of Physics, 2008, v.1106, p.18-25.
ZELKIN, E.G.; KRAVCHENKO, V.F. Atomic Functions in Antenna Synthesis Problems and New Windows. Review. Journal of Communications Technology and Electronics, 2001, v.46, n.8, p.829-857 [Translated from Radiotekhnika and Electronica, 2001, v.46, n.8, p.903-931].
KRAVCHENKO, V.F. Approximation of diagram direction and synthesis of linear radiator on basis of atomic functions. Zarubezhnaya Radioelektronika. Uspekhy Sovremennoy Radioelektroniki, 1996, n.8, p.23-28.
ZELKIN, E.G.; KRAVCHENKO, V.F.; GUSEVSKII, V.I. Constructive Approximation Methods in Antenna Theory. Moscow: Sains-Press, 2005.
RESNIKOFF, H.L.; WELLS, R.O. Wavelet analysis: the scalable structure of information. New York: Springer, 1998.
KRAVCHENKO, V.F.; YURIN, A.V. The application of R-functions theory and wavelets to the boundary value problems solving of the elliptic type. An International Journal Electromagnetic Waves and Electronic Systems, 2009, v.14, n.3, p.4-39.
KRAVCHENKO, V.F.; LABUN’KO, O.S.; LERER, A.M.; SINYAVSKY, G.P. Computing Methods in the Modern Radio Physics. Moscow: Fizmatlit, 2009 [in Russian, ed. by V.F. Kravchenko].
GULYAEV, Y.V.; KRAVCHENKO, V.F.; PUSTOVOIT, V.I. A New class WA-systems of Kravchenko-Rvachev functions. Doklady Mathematics, 2007, v.75, n.2, p.325-332.
GULYAEV, Y.V.; KRAVCHENKO, V.F.; PUSTOVOIT, V.I. Kravchenko-Kotel’nikov analytical wavelets in digital signal processing. Doklady Mathematics, 2007, v.52, n.12, p.645-652.
KRAVCHENKO, V.F.; VOLOSYUK, V.K.; PAVLIKOV, V.V. Digital Signal Processing and Atomic Functions in Synthetic Aperture Radar. Telecommunications and Radio Engineering, 2007, v.66, n.16, p.1441-1452.
KRAVCHENKO, V.F.; SIZOVA, N.D. The R-function method in the investigation of the problems of diffraction of the electromagnetic waves on a system of bodies. Proc. of Sixth Int. Kharkov Symp. on Physics and Engineering of Microwaves, Millimeter and Submillimiter Waves and Workshop on Teraherz Tecnologies. 25-30 June 2007, Kharkov, Ukraine. Kharkov, 2007, v.2, p.929-931.
KRAVCHENKO, V.F.; SMIRNOV, D.V. The form optimization of the ultrashot pulshed signals on basis of atomic functions. Proc. of Sixth Int. Kharkov Symp. on Physics and Engineering of Microwaves, Millimeter and Submillimiter Waves and Workshop on Teraherz Tecnologies. 25-30 June 2007, Kharkov, Ukraine. Kharkov, 2007, v.2, p.971-973.
KRAVCHENKO, V.F.; KRAVCHENKO, O.V.; YURIN, A.V. The contour analysis of low-sized complex-shaped objects based on R-functions, atomic functions and wavelets. Proc. of Sixth Int. Kharkov Symp. on Physics and Engineering of Microwaves, Millimeter and Submillimiter Waves and Workshop on Teraherz Tecnologies. 25-30 June 2007, Kharkov, Ukraine. Kharkov, 2007, v.2, p.974-976.
CHERNOGOR, L.F.; KRAVCHENKO, V.F.; LAZORENKO, O.V. Analytical Kravchenko-Rvachev wavelets based on the atomic functions. Proc. of Sixth Int. Kharkov Symp. on Physics and Engineering of Microwaves, Millimeter and Submillimiter Waves and Workshop on Teraherz Tecnologies. 25-30 June 2007, Kharkov, Ukraine. Kharkov, 2007, v.2, p.983-985.
KRAVCHENKO, V.F.; VOLOSYUK, V.K.; PAVLIKOV, V.V. The Family of Atomic Function and Digital Signal Processing in Synthetic Aperture Radar. Proc. of 6th Int. Conf. on Antenna Theory and Techniques, Sevastopol, ICATT, 17-21 Sept. 2007, Sevastopol, Ukraine. Sevastopol, 2007, p.20-25, DOI: http://dx.doi.org/10.1109/ICATT.2007.4425109.
VOLOSYUK, V.K.; KRAVCHENKO, V.F. Statistical Theory of Radio Technical Systems of Remote Sensing and Radar. Moscow: Fizmatlit, 2008.
KRAVCHENKO, V.F.; YURIN, A.V. The application of the new class of wavelets in digital signal and image processing. Successes of Modern Radio Electronics, 2008, n.5, p.3-64.
KRAVCHENKO, V.F.; CHURIKOV, D.V. Atomic functions ha(x) and new orthogonal wavelets on their basis. Successes of Modern Radio Electronics, 2008, n.6, p.67-88.
KRAVCHENKO, V.F.; PONOMARYOV, V.I.; SANCHEZ-RAMIREZ, J.L. Properties of different wavelet filters used for ultrasound and mammography compression. Telecommunications and Radio Engineering, 2008, v.87, n.10, p.853-865.
KRAVCHENKO, V.F.; SAFIN, A.R. Atomic functions and N-D Whittaker-Kotel’nikov-Shannon theorem. An International Journal Electromagnetic Waves and Electronic Systems, 2008, v.13, n.12, p.31-44.
KRAVCHENKO, V.F.; SAFIN, A.R. Generalized Kravchenko-Fourier Transforms Based On The Atomic Functions. Proc. of 11th Int. Conf. and Exhibition on Digital Signal Processing and Its Applications, 25-27 Mar. 2009, Moscow, Russia. Moscow, 2009, v.1, p.135-137.
KRAVCHENKO, V.F.; KRAVCHENKO, O.V.; SAFIN, A.R. Kravchenko-Rvachev atomic distributions in diffraction theory. Proc. of Int. Conf. on Days on Diffraction, 26-29 May 2009, St.Petersburg, Russia. St.Petersburg, 2009, p.55.
KRAVCHENKO, V.F.; CHURIKOV, D.V. Synthesis of two-dimensional digital filters with non standard geometry of basic area. Successes of Modern Radio Electronics, 2009, n.5, p.3-13.
KRAVCHENKO, V.F.; KRAVCHENKO, O.V.; Safin, A.R. Atomic functions in probability theory and stochastic processes. Successes of Modern Radio Electronics, 2009, n.5, p.23-39.
KRAVCHENKO, V.F.; CHURIKOV, D.V. A new class of orthogonal Kravchenko WA-system functions {ha(t)}. Telecommunications and Radio Engineering, 2009, v.68, n.8, p.649-666.
GOMEZTAGLE, F.; KRAVCHENKO, V.F.; PONOMARYOV, V.I. Super-Resolution method based on wavelet atomic functions in images and video Sequences. Telecommunications and Radio Engineering, 2009, v.68, n.9, p.747-761.
KRAVCHENKO, V.F.; CHURIKOV, D.V. Atomic and R-functions in the synthesis of two-dimentional fir filters. Proc. of 11th Int. Conf. and Exhibition on Digital Signal Processing and Its Applications, 25-27 Mar. 2009, Moscow, Russia. Moscow, 2009, v.1, p.141-144.
GOMEZTAGLE, F.; KRAVCHENKO, V.; PONOMARYOV, V. Super-Resolution Procedures in Images and Video Sequences Applying Wavelet Atomic Functions. Proc. of the 20th IASTED Int. Conf. on Modelling and Simulation, 6-8 July 2009, Banff, Alberta, Canada. 2009, p.187-189.
