Existence Conditions for Discrete Noncanonical Multiwindow Gabor Schemes

A class of noncanonical duals for multiwindow Gabor (MWG) schemes, encompassing both rational and integer oversampling of the Gaborian combined time-frequency space, is considered. Using properties of Gabor frame matrices (GFM), block discrete Fourier transforms (BDFTs), and results from number theory, we use matrix factorization to establish existence conditions for noncanonical duals for both integer and rational oversampling rates, in the signal domain. For comparison and completeness of the results, we also obtain the equivalent results in the finite Zak transform (FZT) domain.