Designing Gabor windows using convex optimization
This work provides a method to design better dual windows for Gabor frames, benefiting signal processing applications that rely on time-frequency analysis.
The authors address the problem that the canonical dual Gabor window may lack desirable properties like time-frequency concentration or smoothness. They use convex optimization to design dual windows with improved features, demonstrating considerable improvements in numerical experiments.
Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal l2-norm dual window, is widely used. This window function however, might lack desirable properties, e.g. 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.