%0 Journal Article %T Designing Gabor windows using convex optimization %A Nathana£¿l Perraudin %A Nicki Holighaus %A Peter L. S£¿ndergaard %A Peter Balazs %J Mathematics %D 2014 %I arXiv %X Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, con- structed from the minimal l2-norm dual window, is widely used. This window function however, might lack desirable properties, such as good time-frequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler-Raz equations and optimizing various constraints. Numerical experiments suggest that alternate dual windows with considerably improved features can be found. %U http://arxiv.org/abs/1401.6033v3