Given a Dirac comb

c(x) = 1/n Σ_i=1^n δ(х - x_i)

Sorry for the pedantry, but a mixture of Dirac distributions is almost always not a Dirac comb. Notice that a mixture of Dirac distributions is a Dirac comb only if you have an infinite number of equally-separated samples (and empirical distributions tend to have a finite number of samples).