Irregular orthonormal Gabor basis in finite dimensions and applications

Gabor analysis is playing an important role in time-frequency analysis for the last 60 years. The fundamental concept of Gabor frames has become a focus also in the finite dimensional setting. Here, we study which sets of discrete time frequency shifts admit a proper choice of window vector, so that they generate an orthonormal Gabor basis in the underlying finite dimensional vector space. We fully characterize such time-frequency shift sets in the case that the vector space dimension is a prime number.