**Abstract: ** I will briefly introduce the Wigner function of the state of a single
optical mode (or a quantum mechanical harmonic oscillator) and related
concepts of characteristic function, Glauber-Sudarshan P- and Hussimi
Q-function. I will review recent generalizations of these concepts to
finite-dimensional Hilbert spaces and to "number-phase" representation of
single optical mode dynamics and the main complications caused by the
different nature of the respective systems. The aim of my talk is to bring
the generalization further to quantum mechanical rotators, or systems
described by angle-angular momentum, and show how almost all aspects of the
theory can in fact be attributed to very general properties of Fourier
transform which is a common link between all the quantum mechanical systems
in question. This could then be used to quickly and effortlessly derive
results for more complicated systems, composite systems etc.