Journal article

Publication year: 2005

Pages: 685-711

Journal: SIAM Journal on Mathematical Analysis

Volume number: 37

Issue number: 3

ISSN: 0036-1410

eISSN: 1095-7154

Open access status: Green

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

Publisher: 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 Citation style: 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 Citation style: 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