This work proposes and studies a new internal model for discrete-time passive or finite-frequency positive-real systems which can be used in repetitive control designs to track or to attenuate periodic signals. The main characteristic of the proposed internal model is its passivity. This property implies closed-loop stability when it is used with discrete-time passive plants, as well as the broader class of discrete-time finite-frequency positive real plants. This work discusses the internal model energy function and its frequency response. A design procedure for repetitive controllers based on the proposed internal model is also presented. Two numerical examples are included.