Signal concentration on unit sphere: An azimuthally moment weighting approach

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.