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Wilson bases for general time-frequency lattices

Gitta Kutyniok·Thomas Strohmer
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Abstract

Motivated by a recent generalization of the Balian-Low theorem and by new research in wireless communications we analyze the construction of Wilson bases for general time-frequency lattices. We show that orthonormal Wilson bases for $\LtR$ can be constructed for any time-frequency lattice whose volume is $\tfrac12$. We then focus on the spaces $\ell^2(\ZZ)$ and $\CC^L$ which are the preferred settings for numerical and practical purposes. We demonstrate that with a properly adapted definition of Wilson bases the construction of orthonormal Wilson bases for general time-frequency lattices also holds true in these discrete settings. In our analysis we make use of certain metaplectic transforms. Finally we discuss some practical consequences of our theoretical findings.

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Gitta Kutyniok, Thomas Strohmer. 2003-11-21. Wilson bases for general time-frequency lattices. https://arxiv.org/abs/math/0311383

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