Tobias Kloos

Technische Universität Dortmund | TUD · Department of Applied Mathematics

The usefulness of Gabor frames depends on the easy computability of a suitable dual window. This question is addressed under several aspects: several versions of Schulz's iterative algorithm for the approximation of the canonical dual window are analyzed for their numerical stability. For Gabor frames with totally positive windows or with exponenti...

We study the Zak transform of totally positive (TP) functions. We use the convergence of the Zak transform of TP functions of finite type to prove that the Zak transforms of all TP functions without Gaussian factor in the Fourier transform have only one zero in their fundamental domain of quasi-periodicity. Our proof is based on complex analysis, e...

Die vorliegende Arbeit behandelt die Anwendung von Schoenbergs total positiven Funktionen, sowie exponentieller B-Splines in der Zeit-Frequenz-Analyse. Wir werden aufzeigen, dass sich diese Funktionen sehr gut als Fenster der Gabor-Transformation eignen und darüber hinaus anwendungsorientierte Algorithmen zur Implementierung angeben. Nach einer ku...

The publisher corrects an editorial error: The correct corresponding editor for this article should be Joseph Ward.

We study totally positive (TP) functions of finite type and exponential B-splines as window functions for Gabor frames. We establish the connection of the Zak transform of these two classes of functions and prove that the Zak transforms have only one zero in their fundamental domain of quasi-periodicity. Our proof is based on the variation-diminish...