Plenacoustic function on the circle with application to HRTF interpolation

The sampling of a sound field using circular microphone arrays is studied. We give a new representation of the sound field sampled on such an array using the two-dimensional Fourier transform. We then show how we can reconstruct the sound field at all possible positions 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 technique is applied to interpolate head related transfer functions (HRTFs) where we also derive an angular sampling theorem.