  We report a detailed investigation of the interplay between size quantization
and local scattering centers in graphene nanoribbons, as seen in the local
density of states. The spectral signatures, obtained after Fourier
transformation of the local density of states, include characteristic peaks
that can be related to the transverse modes of the nanoribbon. In armchair
ribbons, the Fourier transformed density of states of one of the two
inequivalent sublattices takes a form similar to that of a quantum channel in a
two-dimensional electron gas, modified according to the differences in
bandstructure. After addition of the second sublattice contribution, a
characteristic modulation of the pattern due to superposition is obtained,
similar to what has been obtained in spectra due to single impurity scattering
in large-area graphene. We present analytic results for the electron propagator
in armchair nanoribbons in the Dirac approximation, including a single
scattering center within a T-matrix formulation. For comparison, we have
extended the investigation with numerics obtained with an atomistic recursive
Green's function approach. The spectral signatures of the atomistic approach
include the effects of trigonal warping. The impurity induced oscillations in
the local density of states are not decaying at large distance in few-mode
nanoribbons.
