Accurate Extraction of Early-/Late-Time Responses Using Short-Time Matrix Pencil Method for Transient Analysis of Scatterers

We present a new efficient technique for accurately distinguishing the early-time and late-time modes of the transient response from multiscatterer targets. In multiple resonant-based scatterers where the complex natural resonances (CNRs) are used as the ID of the target, the early-time response of the second scatterer might overlap with the late-time of the first, introducing some difficulties in the detection of the second scatterer and additionally, identification of the first one. In such circumstances, the separation of the late-time CNRs (ID of the scatterer) from the early-time poles (scattering centers) is challenging. The smaller the distance between two scatterers, the more difficult the detection process is. Here, by sliding a window along the time axis and applying short-time matrix pencil method (STMPM), the poles corresponding to the early-time and late-time responses are distinguished. It will be shown that when the early-time response is located at the center of the sliding window, its CNRs are located on the imaginary axis of the pole diagram. By monitoring the zero-crossing points in time damping-factor diagram, the locations of the early-time responses (or equivalently scattering centers) can be detected. Some scenarios are discussed, simulated, and confirmed by measurement results to show the effectiveness of the proposed technique in practical applications.