  Spectral weight functions are easily obtained from two-point correlation
functions and they might be used to distinguish single-particle from
multi-particle states in a finite-volume lattice calculation, a problem crucial
for many lattice QCD simulations. In previous studies, it is shown that the
spectral weight function for a broad resonance shares the typical volume
dependence of a two-particle scattering state i.e. proportional to $1/L^3$ in a
large cubic box of size $L$ while the narrow resonance case requires further
investigation. In this paper, a generalized formula is found for the spectral
weight function which incorporates both narrow and broad resonance cases.
Within L\"uscher's formalism, it is shown that the volume dependence of the
spectral weight function exhibits a single-particle behavior for a extremely
narrow resonance and a two-particle behavior for a broad resonance. The
corresponding formulas for both $A^+_1$ and $T^-_1$ channels are derived. The
potential application of these formulas in the extraction of resonance
parameters are also discussed.
