Situational awareness strategies are essential for the reliable and secure operation of the electric power grid which represents critical infrastructure in modern society. With the rise of converter-interfaced renewable generation and the consequent shift towards low-inertia networks, power grids are likely to experience more frequent and severe grid dynamics, necessitating advanced grid monitoring technologies coupled with refurbished protection and control strategies. In response to this challenge, Phasor Measurement Units (PMUs) have become crucial for measurement, control, and protection schemes in power grids, offering accurate, localized, and time-synchronized snapshots of the grid with rapid refresh rates. However, PMUs are based on the stationary, narrowband phasor model which is inherently unsuitable for the analysis of severe signal dynamics and can result in misleading synchrophasor estimations and inappropriate control actions. Within this context, this thesis explores three distinct strategies for the detection and compression of broadband signal dynamics. The first method involves projection of the signal's broadband discrete Fourier spectrum onto parameterized dictionaries to distinguish and identify common signal dynamics. This method yields high-accuracy estimates for long observation windows. However, its effectiveness is limited by the frequency resolution of the discrete spectrum, and its performance decreases for shorter observation windows. Building off of this work, a hybrid time- and frequency-domain method is proposed, leveraging properties of Hilbert transform-derived analytic signals to improve parameter estimation for shorter window lengths. The technique is capable of identifying interfering tones and windows with multiple steps. However, the computational requirements of the method scale rapidly when expanding the parameter ranges or model complexity. For deployment into embedded systems for real-time applications, a third and computationally efficient strategy is proposed which relies on time-domain fitting analysis of the analytic signal components. The technique employs a flexible model, easily accommodates larger parameter ranges, requires only a small set of dictionary elements, and is shown to provide excellent parameter estimations for very short observation windows. A major outcome of the thesis involves the development of a Measurement Unit prototype. Considering the strengths and weaknesses of the proposed methods, the time-domain algorithm is selected and further optimized for deployment onto a dedicated embedded systems device. Efficient, high-performance Hilbert filters are also developed and implemented to estimate the analytic signal. Factors associated with embedded systems, such as latency restrictions, finite memory capacity, and fixed-point precision arithmetic, are taken into account during the deployment process. Finally, the developed prototype is characterized using a PMU calibrator to comprehensively evaluate the algorithm's performance in dynamic conditions, including those specified by and extending beyond the IEC/IEEE 60255/118 Standard requirements. The results of these tests, when compared to standard phasor-based methods, demonstrate the developed tool's potential to detect transients, identify underlying frequency variations, and provide concise, meaningful models for the compression of complex signal dynamics in power systems.