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The sampling of the soundfield using circular microphone arrays is studied. We give a new representation of the soundfield sampled on such an array using the two-dimensional Fourier transform. We then show how we can reconstruct the soundfield at all possible po- sitions on the array from a finite number of measurements. We give the necessary azimuthal angular sampling frequency necessary to reconstruct the data up to some temporal frequency. This new tech- nique is applied to interpolate Head Related Transfer Functions (HRTFs) where we also derive an angular sampling theorem.