The singularity expansion method

Characterization of Perfectly Conducting Targets in Resonance Domain With Their Quality of Resonance

“…The Singularity Expansion Method (SEM) [1,2] provides a convenient methodology, describing the late time response of various scatterers as a finite sum of exponentially damped sinusoids…”

“…SEM was first introduced by Baum [1,2] and was inspired by observing that typical transient temporal responses of various scatterers (e.g. aircrafts, antennas, ...) behave as a combination of exponentially damped sinusoids.…”

Radar Target Discrimination and Identification Using Extinction-Pulses and Single-Mode Extraction Pulses

“…During a finite time period between the onset of late-time and the end of the measured return the convolved output will be a single damped sinusoid of unknown amplitude and phase (depending on target aspect) but known complex frequency. Using the outlined synthesis scheme it is possible to create both sine and cosine S-pulses which result in output convolutions cc(t) and c,(t) with identical unknown amplitudes and unknown phases differing by 900 c,(t) -Aeao°cos(W°t+) (19) which can be combined to form the complex exponential It is apparent that the energy ratio takes on a maximum of unity when the convolved output matches the expected signal. Thus, if the convolutions are corrupted with noise, the ratio closest to unity corresponds to the correct target.…”

“…The complete bibliography is far too lengthy to be included here, but is included in [29]. There are several book chapters and review papers which summarize the major parts of SEN theory [17,19,23,24,45]; one of these summarizes numerical examples of surface currents [19]. Here we also mention the early papers which began SEH [3-5].…”

Ultra wideband radar target discrimination using the signatures algorithm

“…The Baum's singularity expansion method (SEM) [3] where s k = σ k + j2π f k is the k-th aspect-independent natural complex frequency of the target, and A k and ϕ k are the aspect-and excitation-dependent amplitude and phase of the k-th target mode, respectively, w [n] are samples of additive Gaussian band-limited noise. T o describes the period of sampling.…”