Phased array antennas with an arbitrary contour aperture are now becoming more widely used in electronic systems for various purposes. This form of the aperture, in many cases determined by the terms of placement of radiators and/or combining them in a subarrays in order to reduce the number of control channels. In addition, the directional patterns of these antennas may have special requirements which determine, for example, a low level of side lobes and/or special law to the changes in the various directions.

A distinctive feature of the amplitude-phase distribution in any planar aperture is its 2π-periodicity. In addition, this is true of the azimuthal dependence of the formed pattern and patterns of radiators. Accounting for this property and the associated orthogonality the Fourier series can develop a method allowing efficient calculations for solving the amplitude-phase synthesis on a given pattern. The article presents the mathematical basis of the method, we describe the results of numerical studies.