Finite Dimensional Balian-Low Theorems

Applied and Computational Mathematics Seminar
Monday, January 7, 2019 - 1:55pm
1 hour (actually 50 minutes)
Skiles 154
GT Math
Gabor systems, or collections of translations and modulations of a window function, are often used for time-frequency analysis of signals.  The Balian-Low Theorem and its generalizations say that if a Gabor system obeys certain spanning and independence properties in L^2(R), then the window function of such a system cannot be well localized in both time and frequency.  Recently, Shahaf Nitzan and Jan—Fredrik Olsen show that similar behavior extends to Gabor systems of finite length signals in l^2(Z_d).  In this talk, I will discuss these finite dimensional results as well as recent extensions proven in collaboration with Josiah Park.