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Time-frequency shift invariance of Gabor spaces generated by integer lattices (1705.02495v2)
Published 6 May 2017 in math.CA and math.FA
Abstract: We study extra time-frequency shift invariance properties of Gabor spaces. For a Gabor space generated by an integer lattice, we state and prove several characterizations for its time-frequency shift invariance with respect to a finer integer lattice. The extreme cases of full translation invariance, full modulation invariance, and full time-frequency shift invariance are also considered. The results show a close analogy with the extra translation invariance of shift-invariant spaces.