With the expanding role of converter-interfaced distributed energy resources, modern power grids are evolving towards low-inertia networks that are increasingly vulnerable to extreme dynamics. Consequently, advanced signal processing techniques are needed to accurately characterize measured signals in power systems during non-stationary conditions. However, as advocated by recent literature, state-of-the-art phasor estimation methods are unable to sufficiently capture the broadband nature of these signal dynamics since they rely on a quasi-steady state, single tone model. Inspired by previous work by the authors, this paper proposes a signal processing method that uses a dictionary of kernels, modeling common signal dynamics, to compress time-domain information into a few coefficients. The identified signal model and the extracted coefficients capture the broadband spectrum of typical power system signal dynamics and allow for an improved reconstruction of the measured signal.