  The general Weyl -- Wigner formalism in finite dimensional phase spaces is
investigated. Then this formalism is specified to the case of symmetric
ordering of operators in an odd -- dimensional Hilbert space. A respective
Wigner function on the discrete phase space is found and the limit, when the
dimension of Hilbert space tends to infinity, is considered. It is shown that
this limit gives the number -- phase Wigner function in quantum optics.
Analogous results for the `almost' symmetric ordering in an even -- dimensional
Hilbert space are obtained. Relations between the discrete Wigner functions
introduced in our paper and some other discrete Wigner functions appearing in
literature are studied.
