TY - JOUR
T1 - Quadratic variational framework for signal design on the 2-sphere
AU - Wei, Liying
AU - Kennedy, Rodney A.
AU - Lamahewa, Tharaka A.
PY - 2011/11
Y1 - 2011/11
N2 - This paper introduces a quadratic variational framework for solving a broad class of signal design problems on the 2-sphere. The functional, to be extremized, combines energy concentration measures using a weighting function in the spatial domain, multiplicative weights in the spectral domain, and a total energy constraint. This leads to two formulations of the signal design problem on the 2-sphere, one a Fredholm integral equation in the spatial domain and the other an infinite matrix equation in the spectral domain. The framework is illustrated by deriving the key equations for the two classical spatio-spectral concentration problems on the 2-sphere, and for an isotropic filter design that maximizes the filtered energy. In addition, using the proposed framework, we formulate a joint 3-D beamforming application which achieves optimal directivity and spatial resolution simultaneously.
AB - This paper introduces a quadratic variational framework for solving a broad class of signal design problems on the 2-sphere. The functional, to be extremized, combines energy concentration measures using a weighting function in the spatial domain, multiplicative weights in the spectral domain, and a total energy constraint. This leads to two formulations of the signal design problem on the 2-sphere, one a Fredholm integral equation in the spatial domain and the other an infinite matrix equation in the spectral domain. The framework is illustrated by deriving the key equations for the two classical spatio-spectral concentration problems on the 2-sphere, and for an isotropic filter design that maximizes the filtered energy. In addition, using the proposed framework, we formulate a joint 3-D beamforming application which achieves optimal directivity and spatial resolution simultaneously.
KW - Directional derivative
KW - isotropic convolution
KW - uncertainty principle
KW - unit sphere
UR - http://www.scopus.com/inward/record.url?scp=80054077324&partnerID=8YFLogxK
U2 - 10.1109/TSP.2011.2162506
DO - 10.1109/TSP.2011.2162506
M3 - Article
SN - 1053-587X
VL - 59
SP - 5243
EP - 5252
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 11
M1 - 5958643
ER -