In this paper, we study a Lorentzian function based spectral filter suitable for computing highly excited bound states of a quantum system. Using this filter, we have derived an expression for spectral intensities and also implemented a filter diagonalization scheme. We have used a Chebyshev polynomial based series expansion of the filter operator, and this allows us to accomplish a partial resummation of the double series analytically when computing the necessary matrix elements; this saves considerable computational effort. The exponential damping term in the Lorentzian provides a convenient control over the resolution of the computed spectrum in the spectral intensity plot. As a numerical test, we have computed eigenvalues and spectral intensities of a model Hamiltonian in an arbitrary energy window. For situations where eigenvalues are distributed nonuniformly we suggest a computational protocol, which judiciously combines the spectral intensity information with the filter diagonalization method. This protocol is efficient only with the Lorentzian filter studied here. (C) 2003 American Institute of Physics.