Wilson bases for general time-frequency lattices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2003
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| _version_ | 1866908600081842176 |
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| author | Kutyniok, Gitta Strohmer, Thomas |
| author_facet | Kutyniok, Gitta Strohmer, Thomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0311383 |
| institution | arXiv |
| publishDate | 2003 |
| record_format | arxiv |
| spellingShingle | Wilson bases for general time-frequency lattices Kutyniok, Gitta Strohmer, Thomas Functional Analysis Numerical Analysis 94A12; 42C15 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. |
| title | Wilson bases for general time-frequency lattices |
| topic | Functional Analysis Numerical Analysis 94A12; 42C15 |
| url | https://arxiv.org/abs/math/0311383 |