  The objects under inspection, on a given probability space, are noise(-type)
Boolean algebras -- distributive non-empty sublattices of the lattice of all
complete sub-$\sigma$-fields, whose every element admits an independent
complement. Special attention is given to the spectral decompositions of the
algebras of operators generated by the conditional expectations of their
members (acting on $\mathrm{L}^2$).
  Atoms of the spectra are identified in explicit terms. For a reverse
filtration admitting an innovating sequence of equiprobable random signs, a
discreteness property of the spectral measure of the associated noise Boolean
algebra is shown to imply product-typeness.
  Noise projections on the spectral space are introduced, which correspond to
restricting a noise to a part of its domain space. They appear to play a
natural (albeit technical) r\^ole in the general analysis. In particular
through them manifests itself the tensor structure of the spectral
decomposition.
  The spectrum is precisely delineated in the classical case (i.e. when the
noise Boolean algebra is complete), a kind-of standard "symmetric Fock space"
form thereof is procured. The latter result leads to a new characterization of
classicality and blackness involving "spectral independence".
