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In this letter, a procedure based on the spectral rotation is introduced that allows us to calculate the mutual coupling between apertures in the spectral domain without evaluating any convolution products (reaction integral) directly. A numerical evaluation of the computational cost is presented to show the efficiency of the method for electrically large problems. Numerical examples are given to highlight the agreement between the spatial and spectral rotation methods. Finally, the procedure is applied for the de sign of a horn antenna array with rotated apertures.