The previous chapters dealt with the construction and analysis of mathematical models of vibration for mechanical systems composed of concentrated elements of inertia, dissipation, and elasticity. Such models are a priori representations of real life systems. In modern engineering practice, the dynamic behavior of real machines and structures, in terms of output movements and input excitations, can be experimentally recorded using appropriate sensing devices. Mathematical analysis of these signals can be computed to yield experimentally informed, or synthesized, models of the real systems. The present chapter introduces some of the usual mathematical techniques used to perform the analysis of signals from dynamic systems. These techniques serve as aids in the construction of a posteriori, compact models that may also adequately represent the dynamical behavior of these systems.