  We study charmonium correlators at finite temperature using quenched lattice
QCD simulations. Two analysis procedures are applied to extract information on
the spectral function: the maximum entropy method, and the $\chi^2$ fit
analyses including the constrained curve fitting. We focus on the low energy
structure of the spectral function by applying the smearing technique. We first
discuss the applicability of these methods to the finite temperatures by
analyzing the data at T=0 with restricted numbers of degrees of freedom. Then
we apply these methods to the correlators at $T>0$. We find no indication of
mass shift and finite width for the charmonium states at $T\simeq 0.9T_c$. The
results at $T\simeq 1.1 T_c$ imply that bound-state-like structures may survive
even above $T_c$.
