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.