Application of the fractional Fourier transform to the synthesis of low sidelobe pencil shaped beams for nonseparable planar arrays

A technique for the synthesis of low sidelobe pencil shaped beams for nonseparable planar arrays is presented. In order to determine the array excitations a local optimization technique, the truncated-Newton method, is used. The cost function is in part determined from the peak sidelobe values of a series of collapsed one dimensional distributions. The fractional Fourier transform is used to efficiently determine the peak sidelobe values of the collapsed current distributions. For this particular application the fractional Fourier transform is substantially more efficient than the conventional fast Fourier transform.