An open question on the existence of Gabor frames in general linear position

Uncertainty principles for functions defined on finite Abelian groups generally relate the cardinality of a function to the cardinality of its Fourier transform. We examine how the cardinality of a function is related to the cardinality of its short-time Fourier transform. We illustrate that for some cyclic groups of small order, both, the Fourier and the short-time Fourier case, show a remarkable resemblance. We pose the question whether this correspondence holds for all cyclic groups.