So-called Gabor multipliers are particular cases of time-variant filters. Recently, Gabor systems on irregular grids have become a popular research topic. This project deals with Gabor multipliers, as a specialization of frame multipliers on irregular grids.
The initial stage of this project aims to investigate the continuous dependence of an irregular Gabor multiplier on its parameter (i.e. the symbol), window, and lattice. Furthermore, an algorithm to find the best approximation of any matrix (i.e. any time-variant system) by such an irregular Gabor multiplier is being developed.
Gabor multipliers have been used implicitly for quite some time. Investigating the properties of these operators is a current topic for signal processing engineers. If the standard time-frequency grid is not useful to the application, it is natural to work with irregular grids. An example of this is the usage of non-linear frequency scales, like bark scales.
H. G. Feichtinger, NuHAG, Faculty of Mathematics, University of Vienna