New Complex Wavelets Family Based on Atomic Functions

V.F. Kravchenko
Institute of Radio Engineering, Russian Academy of Sciences, Moscow, Russia
Address all correspondence to V.F. Kravchenko E-mail: kvf@pochta.ru

A.Y. Koshelev
N.E. Bauman Moscow State Technical University, Moscow, Russia

Abstract
New Kravchenko-Rvachev complex wavelets built on the base of atomic functions (AF) are proposed and validated. Analytical statements are obtained for the wavelets and their Fourier transforms. The numerical implementation of the AF computation procedures forming the basis of proposed wavelets is considered. The main properties of the Kravchenko-Rvachev complex wavelets are researched and illustrated by numerical experiment.

KEY WORDS: wavelet, atomic function, mathematical approximation, magnitude and phase of signal

References

1. Rvachev, V.L. and Rvachev, V.A., (1979), Unclassical Methods of Approximation Theory in the Boundary-Value Problems. Naukova Dumka, Kiev (in Russian).
2. Kravchenko, V.F., (2003), Lectures on the Theory of Atomic Functions and Their Applications. Radiotekhnika, Мoscow (in Russian).
3. Zelkin, E.G., Kravchenko, V.F., and Gusevsky, V.I., (2005), Constructive Approximation Methods in the Theory of Antennas. Science-Press, Moscow (in Russian).
4. Kravchenko, V.F. and Rvachev, V.L., (2006), Algebra of Logic, Atomic Functions and Wavelets in Physical Applications. Fizmatlit, Moscow (in Russian).
5. Mallat, S.G., (1999), A Wavelet Tour of Signal Processing. Second edition. Academic Press.
6. Blatter, C., (1998), Wavelets – Eine Einführung. Braunschweig/Wiesbaden.

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