TELECOMMUNICATIONS AND RADIO ENGINEERING - 2009 Vol. 68,
No 8 		 

 

 

 

A New Class of Orthogonal Kravchenko WA-System Functions {ha(t)}

V.F. Kravchenko and D.V. Churikov
V.A. Kotelnikov Institute of Radio Engineering and Electronics of RAS, Moscow, Russia

Abstract
On the basis of the ideas set forth in [1-11] construction of the new orthogonal Kravchenko wavelets is considered. This report consists of three parts. In the first part the construction of basic atomic function (AF) is stated and its basic properties are resulted. In the second part basic wavelets on the basis of AF ha(t) are constructing and prove. In the third part the characteristics of new wavelets are analyzed and compared with known following wavelets: the Meyer and Kotelnikov-Shannon ones.

References

  1. Kravchenko, V.F., (2003), Lectures on the Theory of Atomic Functions and Their Some Applications, Publishing House Radio Engineering, Moscow (in Russian).
  2. Kravchenko, V.F., and Rvachov, V.L., (2006), Boolean Algebra, Atomic Functions and Wavelets in Physical Applications. Fizmatlit, Moscow (in Russian).
  3. Gulyaev, Yu.V., Kravchenko, V.F., and Pustovoit, V.I., (2007), A New Class WA-Systems of Kravchenko-Rvachev Functions, Doklady Mathematics, 75(2):325-332 (in Russian)).
  4. Gulyaev, Yu.V., Kravchenko, V.F., and Pustovoit, V.I., (2007), Kravchenko–Kotel’nikov Analytical Wavelets in Digital Signal Processing, Doklady Physics, 52(12):645-652 (in Russian).
  5. Kravchenko, V.F., (ed.) (2007), Digital Signal and Image Processing in Radio Physical Applications, Fiznatlit, Moscow (in Russian).
  6. Mallat, S.G., (1998), A Wavelet Tour of Signal Processing. Academic press. New York.
  7. Meyer, Y., (1992), Wavelets and Operators. Cambridge University Press.
  8. Kravchenko, V.F., and Yurin, A.V., (2008), The Application of The New Class of Wavelets in Digital Signal and Image Processing. Successes of Modern Radio Electronics, 5:3-64 (in Russian).
  9. Kravchenko, V.F., and Churikov, D.V., (2008), Atomic Functions ha(x) and New Orthogonal Wavelets on Their Basis. Successes of Modern Radio Electronics, 6:67-88 (in Russian).
  10. Kravchenko, V.F., Labun’ko, O.S., Lerer, A.M., and Sinyavsky, G.P., (2009), Computing methods in the modern radio physics. Fizmatlit, Moscow (in Russian).
  11. Kravchenko, V.F., and Churikov, D.V., (2008), A new Class of the Orthogonal Kravchenko Wavelets. Proceedings of International Conference RVK08 and MMWP08, Växjö, Sweden, June 9-13, pp.39-43.


pages 649-666

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