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The circular symmetry of concentric ring arrays becomes an advantage for situations where the radiation patterns are symmetric in the azimuthal direction. For planar arrays with elements in an equispaced grid, the fast Fourier transform can be applied in the calculations involved between the array factor and the source distribution. However, for circular arrays the elements are in a non-equispaced grid, making the application of fast computation algorithms difficult. Therefore, two techniques are proposed to synthesize circular arrays. The first one provides the control of the pattern by sampling the array factor. In this case, the fast Fourier transform can be applied. The windows technique is also utilized to control the sidelobe levels and the ripple structure of the shaped beam. The second technique considers the symmetric nature of concentric circular arrays and the control of the array factor is performed imposing some specific points of the pattern.