According to A.~Weil the natural setting for Fourier Analysis (and hence for TFA $=$ Time-Frequency Analysis and Gabor Analysis) are locally compact (LCA) groups. Obviously finite Abelian groups are an important (non-trivial) subclass of this category. While the Euclidean setting ($G = R^d)$ requires the use of integrals and typically Lebesgue spaces and other functional analytic concepts (such as Hilbert spaces, distribution spaces, Banach Gelfand Triples, frames, etc.) Harmonic Analysis boils down to Linear Algebra for the case of finite groups using certain group invariances.
Nevertheless, realizing the general concepts of TFA over LCA groups in this context is not a trivial task, at least if one wishes to keep the connection
with the continuous (non-compact, non-periodic) case. The introductory presentation will highlight a couple of concepts and their realization using MATLAB. The purpose is to demonstrate that almost every concept typically
treated in the Euclidean context can be well simulated nowadays in the finite setting.
The highlights will be the determination of dual Gabor atoms, the creation of Gabor multipliers (known as localization or Anti-Wick operators in the literature) and the determination of eigenvectors of such operators. But there are also methods to create discrete Hermite functions, or obtain the Wigner matrix of a signal of length $N$, for any $N$ (including the even case, which is new).
For the realization of Quantum Harmonic Analysis we need efficient code for the
determination of the Kohn-Nirenberg or spreading representation of a given operator. The demonstration will provide MATLAB Live Scripts which can be shared. If time permits the so-called $Nto4N$-principle will be shortly explained.