Equivalence of two methods for constructing tight Gabor frames

Authors

Augustus J. E. M. Janssen and Helmut Bölcskei

Reference

IEEE Signal Processing Letters, Vol. 7, No. 4, pp. 79-82, Apr. 2000.

Abstract

Recently, in the context of Orthogonal Frequency Division Multiplexing (OFDM) a new method (FAB-method) [11] for constructing tight Gabor frames (with redundancy 2) from a (non-tight) gaussian g was proposed. In this letter, we prove that the FAB-method yields the tight window function canonically associated to the gaussian. We furthermore provide a necessary and sufficient condition on the initial window function g in the Zak transform domain for the FAB-method to yield a tight Gabor frame. This yields a characterization of all initial window functions g for which the FAB-method works.

Keywords

OFDM, Gabor expansions, Weyl-Heisenberg frames, tight frames, Zak transform

Download this document:

Copyright Notice: © 2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.