Radiated or scattered fields are represented as being radiated by a number of limited plane wave spectra obtained by subdividing the 3D spectrum into spectra defined in several planes, using a partition of unity technique. Gabor frame decomposition can be used in each spectral domain, to decompose the field spectrum into Gaussian windows radiating in the form of Gaussian beams. The summation of all beams provides a representation of fields radiated or scattered into all the directions of space. Numerical illustration and validation of this approach will be presented