  The Dirac combs of primitive Pisot--Vijayaraghavan (PV) inflations on the
real line or, more generally, in $\mathbb{R}^d$ are analysed. We construct a
mean-orthogonal splitting for such Dirac combs that leads to the classic
Eberlein decomposition on the level of the pair correlation measures, and thus
to the separation of pure point versus continuous spectral components in the
corresponding diffraction measures. This is illustrated with two guiding
examples, and an extension to more general systems with randomness is outlined.
