Wilson Bases for General Time-Frequency Lattices
نویسندگان
چکیده
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(R) can be constructed for any time-frequency lattice whose volume is 1 2 . We then focus on the spaces l(Z) and C 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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عنوان ژورنال:
- SIAM J. Math. Analysis
دوره 37 شماره
صفحات -
تاریخ انتشار 2005