Propagation of optical signals across a linear–nonlinear interface is investigated by using a spectral decomposition technique involving discrete sideband frequencies. The complexity of the analysis is shown to be appreciably reduced by assuming incommensurate discrete sidebands around the carrier. The efficacy of this formalism is tested for various cases, including discrete stationary modes, evolution of discrete sidebands assuming an undepleted carrier, and, finally, AM pulse propagation across the interface. Among several interesting results, the formation of a narrow-band FM pulse, spatially separated from the ubiquitous AM pulse, is demonstrated. The latter result may be interpreted as a test of the stability of the uniform plane-wave solution.