Quadratic variational framework for signal design on the 2-sphere

Liying Wei*, Rodney A. Kennedy, Tharaka A. Lamahewa

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Article number5958643
    Pages (from-to)5243-5252
    Number of pages10
    JournalIEEE Transactions on Signal Processing
    Volume59
    Issue number11
    DOIs
    Publication statusPublished - Nov 2011

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