Generalized Kravchenko-Kotel´nikov sampling theorem for interpolation of signals with complex shape

The problem of development of controlled radiation patterns (RP) with given form using antenna arrays (AA) with a limited number of elements is relevant. One of the main tasks in this way is the synthesis of AA with the required form of RP (with remaining parameters for a given antenna) with a minimum number of elements. In this work the method of synthesis of AA makes it simple to determine the location of the elements, as well as the magnitude of the currents in the radiators to ensure receipt of the RP, close enough to be given. Methods of approximation of RP, based on the theory of atomic functions (AF) are considered. It is shown that generalized on AF series interpolation better approximate the RP to given. The generalization of this approach (Kravchenko-Kotel´nikov theorem) on 2D-case in the approximation of signals with complex geometry of the emitters is presented.