Equivalence of two methods for constructing tight Gabor frames

Recently, in the context of Orthogonal Frequency Division Multiplexing (OFD M), a new method (FAB-method) [11] for constructing tight Gabor frames (wit h 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 sufficie nt condition on the initial window function g in the Zak transform domain f or the FAB-method to yield a tight Gabor frame. This yields a characterizat ion of all initial window functions g for which the FAB-method works.