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.