Colloquium

Speaker: Professor Alexander Powell (Vanderbilt University)
Title: Uncertainty Principles in Time-Frequency Analysis
Time: 2018-11-01 (Thu.)  15:00 - 16:00
Place: Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Abstract: Gabor systems are a tool for providing practical signal decompositions using the translates and modulates of a given window function. The Balian-Low theorem is a theoretical obstruction which limits how nicely a Gabor system can represent information in the absence of oversampling. Specifically, the classical Balian-Low theorem is a strong form of the uncertainty principle and constrains the time-frequency localization of Gabor systems that form orthonormal bases. We discuss generalizations of the Balian-Low theorem that provide a sharp scale of constraints on the time-frequency localization of Gabor systems under weaker forms of spanning structure associated with so-called Cq systems, and also with Schauder bases. This is joint work with Sara Leshen, Shahaf Nitzan, and Michael Northington.
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