This paper presents an approach to compute couplings between bound and unbound wave functions using only classical Fourier coefficients of the Hamiltonian. This approach is an extension of the well-known technique of using Fourier coefficients in the action-angle representation to compute bound-state to bound-state couplings. We develop the analogous bound-free approach for one-dimensional Hamiltonians and demonstrate it for several coupling potentials. The generalization to higher dimensions is also discussed.