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This paper presents a novel, simple pattern synthesis procedure for linear equispaced arrays which can be characterized by a generalized scattering matrix (GSM) and whose radiated field can be expressed as a weighted sum of shifted spherical waves. It can be viewed as an extension of the classic design techniques of the Fourier series (FS) method or the Woodward-Lawson frequency sampling method, to the case in which the individual antenna elements' patterns and all interelement couplings are taken into account. The design procedure, which yields the excitations needed to achieve the desired pattern, is based on either the FS or the discrete Fourier transform (DFT) of the spherical mode expansion of the array radiated field, as well as on various properties associated to the FS or DFT coefficients. In this work, to compute the GSM of the array and the spherical mode expansion of the field, a validated hybrid full-wave methodology, based on the finite element method and rotation and translation properties of spherical waves, is used. Numerical results of different synthesized array patterns are presented for different arrays made up of dielectric resonator antennas and cavity-backed microstrip circular patches.