Unifying spherical harmonic and 2-D Fourier decompositions of the array manifold

In this paper, a unified framework for orthonormal decomposition of the array manifold is derived. An equivalence between spherical harmonics and 2-D Fourier basis functions is established. Consequently, a link between spherical harmonic spectra and 2-D Fourier spectra is found. Moreover, the spherical harmonic and 2-D Fourier decompositions of the array manifold vector, i.e. Wavefield Modeling and 2-D Effective Aperture Distribution Function (EADF) are shown to be equivalent. The rotation of functions on the 2-D Fourier domain is discussed.