Wilson bases for general time-frequency lattices
Gitta Kutyniok, Thomas Strohmer
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 can be constructed for any time-frequency lattice whose volume is 12. We then focus on the spaces 2() and 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.
Create a lesson
Related papers
Independent Backward Preimages and Algebraic Radial Decompositions of Operators
Zakariae Aznay, Fadil Chabbabi, Hassan Zariouh
Spectral and mapping properties of the inverse Ornstein--Uhlenbeck operator
Tommaso Bruno, Valentina Casarino, Paolo Ciatti et al.
Dual Banach spaces with AP but without BAP
Longfa Sun, Zhenguo Wei, Zhendong Xu et al.
Real alternative Daugavet property without Daugavet property in a separable complex Banach space
Jinghao Huang, Ran Xu
Nonisomorphic separable Banach spaces at Lipschitz distance one
Ryotaro Tanaka
Szegő quasiforms: a Schottky-scheme construction for vertex operator superalgebras
A. Zuevsky