Abstract. A method is presented for performing global spherical harmonic computation by two-dimensional Fourier transformations. The method goes back to old literature (Schuster 1902) and tackles the problem of non-orthogonality of Legendre-functions, when discretized on an equi-angular grid. Both analysis and synthesis relations are presented, which link the spherical harmonic spectrum to a two-dimensional Fourier spectrum. As an alternative, certain functions of co-latitude are introduced, which are orthogonal to discretized Legendre functions. Several independent Fourier approaches for spherical harmonic computation fit into our general scheme.