Journalartikel

Jahr der Veröffentlichung: 2005

Seiten: 685-711

Zeitschrift: SIAM Journal on Mathematical Analysis

Bandnummer: 37

Heftnummer: 3

ISSN: 0036-1410

eISSN: 1095-7154

Open Access Status: Green

DOI Link: https://doi.org/10.1137/S003614100343723X

Verlag: Society for Industrial and Applied Mathematics

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 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.

Harvard-Zitierstil: Kutyniok, G. and Strohmer, T. (2005) Wilson bases for general time-frequency lattices, SIAM Journal on Mathematical Analysis, 37(3), pp. 685-711. https://doi.org/10.1137/S003614100343723X

APA-Zitierstil: Kutyniok, G., & Strohmer, T. (2005). Wilson bases for general time-frequency lattices. SIAM Journal on Mathematical Analysis. 37(3), 685-711. https://doi.org/10.1137/S003614100343723X