A derivation of the coordinate representation of the q-deformed oscillator is given. The Hilbert space associated with it is defined on a finite coordinate space y: (-\ensuremath{\pi}/2s,\ensuremath{\pi}/2s), where s is related to the deformation q via q=exp(-
s2), with the respective ``coordinate'' and ``momentum'' operators given by X${\mathrm{^}}_{\mathit{s}}$=y-
As(y), P${\mathrm{^}}_{\mathit{s}}$=-id/dy-
iAs(y), where
As(y)=1/2d ln${\mathrm{\ensuremath{\sigma}}}_{\mathit{s}}$(y)/dy, ${\mathrm{\ensuremath{\sigma}}}_{\mathit{s}}$ being a measure in this space. The commutation rule obeyed by them is X${\mathrm{^}}_{\mathit{s}}$P${\mathrm{^}}_{\mathit{s}}$-P${\mathrm{^}}_{\mathit{s}}$X${\mathrm{^}}_{\mathit{s}}$=i${\mathrm{\ensuremath{\Elzxh}}}_{\mathit{s}}$(y)=i{1-
dAs /dy}. After constructing a suitable representation in the momentum space, we also set up the Wigner distribution function in this phase space. A brief discussion of these results and their interpretation are given.