The behaviour of the eigenfunctions and eigenvalues, that are used to describe the eigenfunction expansion of the receiver decision variable of an optical direct detection differential phase-shift keying (DPSK) system with optical amplification, is analysed for various receiver configurations, and their impact on system performance is investigated. In particular, special attention is given to the ideal receiver, based on an ideal optical filter and an electrical integrate-and-dump filter, to the Gaussian receiver, based on Gaussian shaped filters for both the optical and electrical filters, and to a receiver configuration based on a Lorentzian optical filter and an electrical RC filter.