V. F. Kravchenko, D. V. Churikov

The synthesis algorithm of two-dimensional digital filters by a method of weight functions with geometry of complex shaped support areas based on R-functions is offered and proved. The problem of synthesis of such filters is actual in many applied areas of physics and techniques. First of all it concerns a radar-location, communication, transfers of the digital information, signal processing etc. Thus special attention by developers of equipment is given to spectral properties of these devices. It is known that the most widespread forms of support areas are following: round, rectangular, and hexagonal. In connection with active development of computer facilities and specialized processors there is an interest to synthesis of filters with difficult geometry of support area. The purpose of the given work is development, substantiation and application of the theory of R-functions (Rvachev functions) to considered problems. The universal algorithm allowing us to project the synthesized digital filters with support area of complex shape is offered and proved. Filters with complex shaped support area of can find wide application in problems of recognition, coding and filtration of signals of various physical nature

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