Effective waveform representation of responsive signals initiated by impulsive actions in physical and engineering systems

We report applications of a signal decomposition method based on a basic shock waveform to a wide range of dynamical response signals initiated by impulsive actions in physical and engineering systems. The generality and significance of the shock waveform are demonstrated for time-series signals in different physical and engineering systems disturbed by impulsive actions due to various causes. Case examples include, but are not limited to, signals of heartbeat, earthquake, gravitational wave of binary coalescence, Enhanced Long Range Navigation System (Loran), and mechanical and pyrotechnic shocks. The simplicity of the shock waveform can facilitate the understanding of the intrinsic pattern of the signal and the intrinsic characteristics of the system.