The Balian–Low theorem for a new kind of Gabor system

Abstract

The Balian–Low theorem expresses the fact that time–frequency concentration is incompatible with non-redundancy for Gabor systems. In this article, the Balian–Low theorem is established for a new kind of Gabor systems associated with a phase function θ(t) satisfying certain assumptions. Meanwhile, some properties of the corresponding generalized Zak transform are shown and explicit examples of the phase function θ(t) are provided.