Gabor dual windows using convex optimization reproducible reasearch

Abstract

Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal \(l_2\)-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.

Availlable in this package

In this package, you will find all the experiment done in the paper and some additional one. The code is also availlable and is mostly well documented.

You can also want the convergence of the algorithm at https://lts2research.epfl.ch/rrp/gdwuco/gif.php.

Availlable experiments

• rr_gaboptdual - Presentation of different optimization schemes
• rr_gaboptdual2 - Presentation of different optimization schemes 2
• rr_gaboptdual3 - Presentation of different optimization schemes 3
• rr_gaboptdual_smoothness - Concentration optimization
• rr_gabfirdual_smoothness - Concentration optimization in the FIR case
• rr_gabfirdual_smoothness2 - Concentration optimization in the FIR case 2
• rr_gabfirdual_smoothness3 - Concentration optimization in the FIR case 3
• rr_gabfirdual - Construction of dual FIR window in the non painless case
• rr_gabfirtight - Construction of a tight FIR window
• rr_beat_itersine - Construction of a pair of dual windows
• rr_tradeoff_smoothness - Tradeoff of concentration

For help, bug reports, suggestions etc. please send email to nathanael (dot) perraudin (at) epfl (dot) ch