  By using the localized character of canonical coherent states, we give a
straightforward derivation of the Bargmann integral representation of Wigner
function (W). A non-integral representation is presented in terms of a
quadratic form V*FV, where F is a self-adjoint matrix whose entries are
tabulated functions and V is a vector depending in a simple recursive way on
the derivatives of the Bargmann function. Such a representation may be of use
in numerical computations. We discuss a relation involving the geometry of
Wigner function and the spacial uncertainty of the coherent state basis we use
to represent it.
