  Given a discrete time sample $X_1,... X_n$ from a L\'evy process
$X=(X_t)_{t\geq 0}$ of a finite jump activity, we study the problem of
nonparametric estimation of the characteristic triplet $(\gamma,\sigma^2,\rho)$
corresponding to the process $X.$ Based on Fourier inversion and kernel
smoothing, we propose estimators of $\gamma,\sigma^2$ and $\rho$ and study
their asymptotic behaviour. The obtained results include derivation of upper
bounds on the mean square error of the estimators of $\gamma$ and $\sigma^2$
and an upper bound on the mean integrated square error of an estimator of
$\rho.$
