Hyperbolic secants yield Gabor frames

A. J. E. M. Janssen, Thomas Strohmer

We show that $(g_2,a,b)$ is a Gabor frame when $a>0,b>0,ab<1$ and $g_2(t)=(1/2\pi \gamma {)}^{1/2}(\cosh \pi \gamma t{)}^{-1}$ is a hyperbolic secant with scaling parameter $\gamma >0$. This is accomplis…