The multidimensional multi-window nonrectangular discrete Gabor schemes

The multi-window Gabor (1946) type scheme is generalized to the multidimensional case with special emphasis on nonrectangular lattices. The formulations are presented by means of matrix operations, which incorporate periodicity and sampling matrix that sample the continuous signal over different grids, such as hexagonal grids. The proposed scheme is discussed in the context of oversampling. Algorithms are presented in the Zak transform domain.