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As power grids transition towards low-inertia net-works based on converter-interfaced renewable energy resources, they become increasingly vulnerable to extreme dynamics. Currently, the most advanced methods for signal processing in power systems are embedded in Phasor Measurement Units (PMUs), which rely on a stationary phasor model with a single fundamental tone. However, the signal dynamics measured during grid disturbances may have broadband spectra that cannot be sufficiently captured by a narrowband phasor model. Inspired by previous work done by the authors, this paper introduces a signal processing method based on a dictionary containing models of common signal dynamics. The dictionary can be used to identify the signal model and parameters that best capture the dynamics. The method is evaluated and compared to a standard phasor-estimation method for two documented, real-world grid disturbances.