Power grid operation continuously undergoes state transitions caused by internal and external uncertainties, e.g., equipment failures and weather-driven faults, among others. This prompts an observation of different types of waveforms at the measurement points (substations) in power systems. Modern power systems utilize phasor measurement units (PMUs) and intelligent electronic devices embedded with PMU functionality to capture the corresponding peculiarities through synchrophasor measurements. However, existing PMU devices are equipped with only one synchrophasor estimation algorithm (SEA) and are, thus, not always robust to handle different types of signals across the network. This article proposes a PMU-embedded framework that ensures real-time grid surveillance and potentially enables adaptive selection of preinstalled SEAs in the PMU. Therefore, it ensures high-fidelity measurements at all times and irrespective of the input signals. Our proposed framework consists of: 1) a pseudocontinuous quadrature wavelet transform which generates the featured scalograms and 2) a convolutional neural network for event classification based on the extracted features in the scalograms. Our experiments demonstrate that the proposed framework achieves high classification accuracy on multiple types of prevailing events in power grids, through which an enhanced grid-scale situational awareness in real time can be realized.