V. F. Kravchenko, O. V. Kravchenko, A. R. Safin, D. V. Churikov
In this paper for the first time new designs of weight functions (WF) witch constructed on basis of the probability Kravchenko distributions in respect to problems of digital signal and image processing are considered and proved. For research of WF we used the following modified physical characteristics: relative position of spectral density function (SDF) first zero, relative SDF width on level -6 dB, coherent amplification, the equivalent noise band, maximum level of side lobes, incidental amplitude modulation, maximum conversion loss. Time and frequency distributions of new probabilistic weight functions are also research. The orthogonal wavevlets on basis of new weight functions are constructed. The offered wavevlets and their foundation in the class of the Riesz basis is spent. Numerical experiments show that the new wavelets are better than Meyer wavelet. Analytical wavelet is defined by spectral modulation of weight functions. The basic requirement when constructing analytical wavelet is good enough localization both in time and in frequency areas. This transformation does not influence width of the support interval in the time area. An application of the Kravchenko-Wigner transformations witch based on probability WF in quantum mechanic and optics are considered. A great number of numerical experiments carried out and also an analysis of physical results show efficiency of the suggested and proved new probabilistic weight functions in various problems of digital signal and image processing, radio physics, radar, radio vision, quantum mechanics.
The investigations were supported by grant NSh-5708.2008.9.