In digital recording systems, the total amount of data-dependent media noise increases considerably as recording densities increase. A proper noise characterization is crucial for the design of receivers for high-density storage systems. This characterization involves the selection of a proper noise model and subsequently the accurate estimation of the parameters of the selected model. The estimation algorithm proposed in this paper jointly estimates the parameters of both media and additive noise with a high accuracy. The proposed algorithm makes use of the data dependency of the media noise to distinguish between the different noise sources. The algorithm is simple and as a result can be implemented in recording systems, with only a limited amount of complexity, as an easy "add-on" to read-channel ICs. From the simulation results and the analytical derivation of the estimation algorithm, we can clearly indicate which data patterns yield near-optimal estimation performance. These patterns are the ideal test patterns in experimental systems. We propose and discuss test patterns for magnetic and optical storage systems.