  Within the phase fluctuation picture for the pseudogap state of a
high-$T_{c}$ superconductor, we incorporate the phase fluctuations generated by
the classical XY model with the Bogoliubov-de Gennes formalism utilizing a
field-theoretical method. This picture delineates the inhomogeneous
characteristics of local order parameters observed in high-$T_{c}$
superconductors above $T_{c}$. We also compute the local density of states near
a non-magnetic impurity with a strong scattering potential. The resonance peak
smoothly evolves as temperature increases through $T_{c}$ without showing any
sudden broadening, which is consistent with recent experimental findings.
