  Noise correlations are studied for systems of hard-core bosons in
one-dimensional lattices. We use an exact numerical approach based on the
Bose-Fermi mapping and properties of Slater determinants. We focus on the
scaling of the noise correlations with system size in superfluid and insulating
phases, which are generated in the homogeneous lattice, with period-two
superlattices and with uniformly distributed random diagonal disorder. For the
superfluid phases, the leading contribution is shown to exhibit a
density-independent scaling proportional to the system size, while the first
subleading term exhibits a density-dependent power-law exponent.
