  This paper proposes a new class of copulas which characterize the set of all
twice continuously differentiable copulas. We show that our proposed new class
of copulas is a new generalized copula family that include not only asymmetric
copulas but also all smooth copula families available in the current
literature. Spearman's rho and Kendall's tau for our new Fourier copulas which
are asymmetric are introduced. Furthermore, an approximation method is
discussed in order to optimize Spearman's rho and the corresponding Kendall's
tau.
