Application of the matrix pencil method for estimating the SEM (singularity expansion method) poles of source-free transient responses from multiple look directions

The matrix pencil method has been utilized for estimating the natural resonances from different transient responses recorded along multiple look directions as a function of time after the incident field has passed the structure. The novelty of this article is that a single estimate for all the poles are done utilizing multiple transient waveforms emanating from the structure along multiple look directions. The SEM poles are independent of the angle at which the transient response is recorded. The only difference between the various waveforms are that the residues at the various poles are of different magnitudes. Some of the residues may even be zero for some of the poles indicating that the contribution from certain SEM poles may not be significant along that look direction. Here all the waveforms are utilized providing a single estimate for the poles without performing an arithmetic mean of the various waveforms.