Spectral power distribution using time-varying operators

In this paper we consider the ability of a linear time-varying system to move energy from one frequency to another. After introducing a natural notion of rate-of-variation for linear time-varying operators, we give necessary and sufficient conditions on the rate-of-variation required of a bounded linear operator to map a given input to a given output, modulo l₂ signals. This result has applications in model validation, and in robustness analysis with time-varying uncertainty.