Practical Implications of Pole Series Convergence and the Early-time in Transient Backscatter.

摘要

Here we consider the convergence of the singularity expansion method (SEM) pole series representation of the transient backscatter in terms of the stability in the estimated poles from the time domain response. Using a numerically simulated backscattered response of a thin wire, the temporal progression of the estimated pole series is examined by iteratively estimating them (using the Matrix Pencil Method) at different time-window locations. The results show a good agreement with the well established SEM theory (i.e., a stable set of poles are obtained after the theoretically defined time for convergence). This iterative approach could allow for a more accurate estimation of the poles that represent the resonances of the object. We also consider the use of the 'non-converging' poles estimated in the early-time to approximately represent the early-time specular response.