Uncertainty principle for Gabor systems and the Zak transform

Journal Article · Fri Dec 15 00:00:00 EST 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2393146· OSTI ID:20861566

Czaja, Wojciech; Zienkiewicz, Jacek ^[1]

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1. Institute of Mathematics, University of Wrodaw, Plac Grunwaldzki 2/4, 50-384 Wrodaw (Poland)

We show that if g(set-membership sign)L{sup 2}(R) is a generator of a Gabor orthonormal basis with the lattice ZxZ, then its Zak transform Z(g) satisfies {nabla}Z(g)(negated-set-membership sign)L{sup 2}([0,1){sup 2}). This is a generalization and extension of the Balian-Low uncertainty principle.

• OSTI ID: 20861566
• Journal Information: Journal of Mathematical Physics, Vol. 47, Issue 12; Other Information: DOI: 10.1063/1.2393146; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
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