Title :
On spectral concentration of signals on the 2-sphere under a generalized moment weighting criterion
Author :
Liying Wei ; Kennedy, Rodney A.
Author_Institution :
Coll. of Eng. & Comput. Sci., Australian Nat. Univ., Canberra, ACT, Australia
Abstract :
This paper formulates a spatially-limited signal energy concentration problem on the 2-sphere using a generalized moment criterion in the spectral domain. The set of optimal signals with maximum concentration for general positive spherical harmonic coefficient frequency weightings is obtained. Numerically solving the resulting integral equation optimization shows that this set of functions not only decays slower but also has higher sidelobes than the set of spherical Slepian functions. This result on the 2-sphere contrasts with the findings from the time-frequency analogy which compares the classical Slepian eigenfunctions with the minimum bandwidth basis functions for the fourth-moment bandwidth measure.
Keywords :
harmonic analysis; integral equations; method of moments; optimisation; signal processing; spectral-domain analysis; time-frequency analysis; 2-sphere; Slepian eigenfunctions; fourth-moment bandwidth measure; general positive spherical harmonic coefficient frequency weightings; generalized moment weighting criterion; integral equation optimization; minimum bandwidth basis functions; spatially-limited signal energy spectral concentration problem; spectral-domain analysis; spherical Slepian functions; time-frequency analogy; Eigenvalues and eigenfunctions; Frequency modulation; Harmonic analysis; Integral equations; Spectral analysis; Time-frequency analysis;
Conference_Titel :
Signal Processing Conference, 2010 18th European
Conference_Location :
Aalborg