  We study, both theoretically and experimentally, modulational instability in
optical fibers that have a longitudinal evolution of their dispersion in the
form of a Dirac delta comb. By means of Floquet theory, we obtain an exact
expression for the position of the gain bands, and we provide simple analytical
estimates of the gain and of the bandwidths of those sidebands. An experimental
validation of those results has been realized in several microstructured fibers
specifically manufactured for that purpose. The dispersion landscape of those
fibers is a comb of Gaussian pulses having widths much shorter than the period,
which therefore approximate the ideal Dirac comb. Experimental spontaneous MI
spectra recorded under quasi continuous wave excitation are in good agreement
with the theory and with numerical simulations based on the generalized
nonlinear Schr\"odinger equation.
