An efficient analysis technique for a transmitarray (TA) unit cell based on a method of moments (MoM) in the spectral domain assuming local periodicity is proposed. The MoM employs basis functions consisting of Chebyshev polynomials weighed by a function that accounts for edge singularities. The analysis technique is applied to a unit cell consisting of two sets of five parallel dipoles that are shifted one with respect to the other to create a Huygens resonance that maximizes transmission of the impinging plane wave. Comparisons with circuit models show that the proposed technique achieves better accuracy while providing significant computational gains compared with commercial general purpose software. Finally, a unit cell is optimized to work in the W-band with the aim of employing it to the design of TAs for ultra-capacity fixed wireless links.