Calculating the dual Gabor window for general sampling sets

Methods for the calculation of the so-called dual Gabor window for general sampling sets are developed. First, we consider the standard situation where the time-frequency plane (TF-plane) is (over)sampled on a grid, i.e., a rectangular lattice is considered with more points than the dimension of the signal space. Second, we show that the proposed method can be easily extended to general subgroups of the TF-plane. One typical example of such a sampling set is the so called quincunx-lattice