We present a new and more general theory of discrete Gabor expansions for arbitrary dimensional spaces. We show that a discrete Gabor expansion is in fact a general frame decomposition. We provide a complete characterization of all possible discrete Gabor expansions. We reveal an intrinsic dimension invariance property of the (discrete) Gabor expansion. We derive a parametric algorithm for computing all analysis waveforms that are dimension independent. We shall also consider the issue of optimum Gabor expansion and the construction of non-separable 2D discrete Gabor expansions.
"General theory of discrete Gabor expansion", Proc. SPIE 2303, Wavelet Applications in Signal and Image Processing II, (11 October 1994); doi: 10.1117/12.188777; https://doi.org/10.1117/12.188777