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.