  A generalized Weyl quantization formalism for a particle on the circle
investigated in \cite{1} is developed. A Wigner function for the state
$\hat{\varrho}$ and the kernel $\mathcal{K}$ for a particle on the circle is
defined and its properties are analyzed. Then it is shown how this Wigner
function can be easily modified to give the number-phase Wigner function in
quantum optics. Some examples of such number-phase Wigner function are
considered.
