This thesis explores the analysis of moving objects in video frames by introducing a novel method for motion signal representation and self-similarity detection. The focus is on identifying and characterizing motion signals generated by vibrating objects within the frames, specifically tracking the center of motion and extracting the corresponding row of pixel values, referred to as the motion signal. Traditional approaches to signal processing often rely on basic pixel-based representations, which can miss the intricate dynamics of vibrating objects. In contrast, the proposed methodology leverages signal modulation, energy calculation, and cross-correlation to analyze the self-similarity of motion signals. The methodology begins by extracting the motion signal from the vibrating object, modulating it to enhance periodic features. Small variations are filtered by applying a threshold, and energy is calculated to assess the object’s dynamics. Limit points, defined as the maximum values on the motion signal, are detected in each frame, and the rate of change (ROC) is calculated based on the variations of these limit points. The cross-correlation method is then employed to determine self-similarity in the signal, focusing on the correspondence between positive and negative lobes. This research advances video signal processing by providing a robust framework for analyzing and comparing motion signals of vibrating objects. The insights gained enhance the understanding of vibration patterns and variations in limit points, with potential applications in detecting uneven mechanical vibrations, monitoring excessive movements in athletes, or identifying anomalies in vibrating systems.