We present a method for analyzing and classifying 2d-pure-point (pp) diffraction spectra (i.e. set of Bragg peaks)
of certain self-similar structures with scaling factor β > 1, like quasicrystals. The 2d-pp diffraction spectrum is
viewed as a point set in the complex plane in which each point is assigned a positive number, its Bragg intensity.
Then, by using a nested sequence of self-similar subsets called
beta-lattices, a multiresolution analysis is carried
out on the spectrum, leading to a partition of it at once in geometry, in scale, and in intensity ("fingerprint" of
the spectrum). As an illustration of our approach, the method is experimented on pp diffraction spectra of a
few mathematical structures.