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A new compact model is described for the 3D radiation pattern of an ultrawideband antenna, using a vector spherical and Slepian decomposition. Vector spherical modes are known to provide a good basis for the angular dependency of the radiation pattern. This paper is the first to extend such a model to also incorporate the frequency dependency of a radiation pattern. This is achieved by using a Slepian mode expansion. It is shown that this model requires considerably less coefficients than traditional sampling to accurately describe a frequency-dependent 3D radiation pattern. Also, generating the Slepian modes is computationally more efficient than comparable techniques, such as the singularity expansion method (SEM). The coefficients can then directly be used to efficiently calculate performance measures such as the antenna fidelity factor for all angles (??,??) without reconstructing the radiation pattern, or to reduce the noise contribution.