Abstract
We show that (g2,a,b) is a Gabor frame when a > 0, b > 0, ab<1, and g2(t)=(12p¿)1/2(coshp¿t) -1 is a hyperbolic secant with scaling parameter ¿>0. This is accomplished by expressing the Zak transform of g2 in terms of the Zak transform of the Gaussian g1(t)=(2¿)1/4 exp(-p¿t2), together with an appropriate use of the Ron-Shen criterion for being a Gabor frame. As a side result it follows that the windows, generating tight Gabor frames, that are canonically associated to g2 and g1 are the same at critical density a=b=1. Also, we display the "singular" dual function corresponding to the hyperbolic secant at critical density.
Original language | English |
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Pages (from-to) | 259-267 |
Number of pages | 9 |
Journal | Applied and Computational Harmonic Analysis |
Volume | 12 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2002 |