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

CABRELLI, CARLOS A.; LEE, DAE GWAN; MOLTER, URSULA M.; PFANDER, GOETZ

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2019 vol. 474 p. 1289 - 1305

0022-247X

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.