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 L^2(R)$ can be constructed for any time-frequency lattice whose volume is $1/2$. We then focus on the spaces l^2(Z) and C^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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