We introduce a generalization of local density of states which is "windowed"
with respect to position and energy, called the windowed local density of
states (wLDOS). This definition generalizes the usual LDOS in the sense that
the usual LDOS is recovered in the limit where the position window captures
individual sites and the energy window is a delta distribution. We prove that
the wLDOS is local in the sense that it can be computed up to arbitrarily small
error using spatial truncations of the system Hamiltonian. Using this result we
prove that the wLDOS is well-defined and computable for infinite systems
satisfying some natural assumptions. We finally present numerical computations
of the wLDOS at the edge and in the bulk of a "Fibonacci SSH model", a
one-dimensional non-periodic model with topological edge states.