Spatially-Limited Sampling of Band-Limited Signals on the Sphere

Abstract

To support the applications where the measurements can only be taken over spatially limited region on the sphere due to practical limitations, we design a spatially-limited sampling scheme on the sphere for the computation of spherical harmonic transform (SHT) of band-limited signals. By enclosing the inaccessible region with the (anisotropic) ellipsoidal region followed by the rotation of the region to the pole or the equator, we propose an iso-latitude sampling scheme on the sphere. We also present a method to place the samples over the spatially-limited region such that the SHT can be computed accurately. Moreover, we formulate the SHT associated with the proposed sampling scheme and analyse its accuracy through numerical experiments. We also provide an illustration where we reconstruct the head-related transfer function (HRTF) from spatially-limited measurements and demonstrate that the proposed sampling design enables more accurate computation than the existing sampling schemes.