Signal Concentration on Unit Sphere: An Azimuthally Moment Weighting Approach

Abstract

Signals defined on the unit sphere cannot be simultaneously concentrated in a spatial region and in the spherical harmonic spectrum. In this paper we develop a unique spatial concentration measure, a kth moment azimuthal measure, for real-valued spectral-limited signals defined on the unit sphere. The optimal functions with the 2nd and 4th minimum azimuthally moment weighting are obtained and simulation results show: 1) the waveforms tend to be even as k increases, 2) have good energy concentration in the spatial region, and 3) have better decaying tails than spherical Slepian functions, which form the benchmark set of basis functions for spherical filter design. Show more