V. F. Kravchenko, V. I. Pustovoit, D. V. Churikov

On the basis of the theory of atomic and R- functions analytical two-dimensional wavelets (2DWA) of Kravchenko-Rvachev (KR) with non-standard geometry of reference area are constructed. It is known that such basic areas take place in a problems of time-space processing, multidimensional digital filtration and the signal spectral analysis of the various physical nature. Given article consists of three parts. In the first part using the theory of R-functions the technique of objects with the complex form description is proved. In the second part new algorithms for construction of analytical 2DWA KR are offered and proved. In the third part the numerical experiment is made and the physical analysis is given. The received results confirm potential possibilities of 2DWA KR. As experiment shows the choice of parameters allows to analyze corresponding frequency ranges of signals and selection of reference area in frequency space concretizes borders of these ranges. At definition of basic area in time space there is a possibility to focus of wavelet-transform on geometrical features of the image and to consider the form of objects. It allows to expand essentially a wavelet-analysis scope, and also to optimize digital processing of multidimensional signals at the expense of simultaneous performance several operation (filtration, allocation of contours and the others). Therefore 2DWA KR can find wide application in problems of the analysis of interferential effects with the geometry of complex form, signal filtration and image recognition.