Wilson Bases for General Time-Frequency Lattices

Kutyniok, Gitta und Strohmer, Thomas (2005): Wilson Bases for General Time-Frequency Lattices. In: SIAM Journal on Mathematical Analysis, Vol. 37, No. 3: pp. 685-711

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 L2(R) general time-frequency lattices. We show that orthonormal Wilson bases for can be constructed for any time-frequency lattice whose volume is 1/2. We then focus on the spaces l2(Z) and CL 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0036-1410
• Language: English