(Non-)existence of Wilson bases for general time-frequency lattices
Year: 2003
Type: preprint
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 L2 (R) can be constructed for any time-frequency lattice whose volume is 1. While this may be expected, our second result may come as a surprise. 2 Namely we prove that there cannot exist Wilson bases (orthogonal or non-orthogonal) for general non-rectangular time-frequency lattices for ℓ2 (Z) nor for the finite case CL. These results should be compared to the fact that tight Gabor frames for general time-frequency lattices exist in abundance for L2 (R), ℓ2 (Z), and CL. We discuss some practical consequences of our theoretical findings. Key words. Wilson basis, metaplectic transform, Gabor frame, Schrödinger representation, time-frequency lattice
Source: arXiv (Cornell University)
Authors: Gitta Kutyniok, Thomas Strohmer
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2803698154