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

DOI: 10.1109/97.833003

[BibTeX, LaTeX, and HTML Reference]

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


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