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

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~{s}ᵢon the integral square error such that lim(ε = 0) ~{s}ᵢ → {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.