  We study the mechanisms responsible for quantum diffusion in the
quasiperiodic kicked rotor. We report experimental measurements of the
diffusion constant on the atomic version of the system and develop a
theoretical approach (based on the Floquet theorem) explaining the
observations, especially the ``sub-Fourier'' character of the resonances
observed in the vicinity of exact periodicity, i.e. the ability of the system
to distinguish two neighboring driving frequencies in a time shorter than the
inverse of the difference of the two frequencies.
