  A fast spectral-domain method is proposed to evaluate the reaction terms
between the Macro Basis Functions in regular and non-regular arrays made of
identical printed antennas. The presented technique first exploits the
filtering capabilities of the Macro Basis Functions in the spectral domain. The
method is then strongly accelerated with the help of a newly formulated Fast
Fourier Transform-based technique, which is applicable to a contour integration
in the complex plane. We name the method as Contour-FFT or C-FFT. Besides an
effective homogeneous medium term treated with multipoles, a computational
complexity of order N log_2 N is achieved for the the tabulation of
substrate-related reaction terms for any possible relative positions. The
complexity of the proposed method is independent from the complexity of the
elements. Numerical results obtained with the proposed method are compared with
those from a pre-validated reference solution based on the traditional Macro
Basis Functions technique; an excellent agreement is observed.
