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We study extra time-frequency shift invariance properties of Gabor spaces.For a Gabor space generated by an integer lattice, we state and prove severalcharacterizations for its time-frequency shift invariance with respect to afiner integer lattice. The extreme cases of full translation invariance, fullmodulation invariance, and full time-frequency shift invariance are alsoconsidered. The results show a close analogy with the extra translationinvariance of shift-invariant spaces.

Time-frequency shift invariance of Gabor spaces generated by integer lattices