Felix Krahmer, Götz E. Pfander, Peter Rashkov

• The uncertainty principle for functions on finite Abelian groups provides us with lower bounds on the cardinality of the support of Fourier transforms of functions of small support. We discuss novel results in this realm and generalize these to obtain results relating the support sizes of functions and their short-time Fourier transforms. We then apply these results to construct a class of equal norm tight Gabor frames that are maximally robust to erasures. We discuss consequences of our findings to the theory of recovering and storing signals with sparse time-frequency representations.