Computing of antenna arrays with an unified theory

The Fourier relation theory, developed by the authors, relates the array factor of an antenna array with the source distribution through the Fourier transform. In this paper, it will be demonstrated that some very well known deterministic synthesis methods of continuous and discrete antenna arrays are particular applications of this theory. Furthermore, using a method based on the Fourier relation, that involves the utilisation of the fast Fourier transform, it is possible to reduce much of the work done in the analysis and synthesis of antenna arrays. With the correct application of this theory, the numeric results obtained to the known synthesis methods are exact, unless the internal error of the used computer, or the error obtained in the approximations are directly controlled to the desired values. As it will be shown, the method presented in this paper is a fundamental tool to lead with the synthesis problem of antenna arrays.