Suboptimal approximation/identification of transient waveforms from electromagnetic systems by pencil-of-function method

Abstract

A noniterative method for approximating signals by a linear combination of exponentials is presented. Although the technique results in a suboptimal approximation, the continuous dependence of the suboptimal exponents \sim{s}_{i} on the integral square error \epsilon is such that lim (\epsilon = 0) \sim{s}_{i} \rightarrow {s}_{i} , the best least squares exponents. The method is also useful for system identification, where the system is modeled by a black box and one has access only to the input and output terminals. A technique is demonstrated for finding the multiple poles of a system along with the residues at the poles when the system output to a known input is given. Advantages of the method are natural insensitivity to noise in the data and a capability for approximately determining signal order. Representative computations are made of the poles from the transient response of a conducting pipe tested at the ATHAMAS-I EMP simulator.