Abstract
The problem of modeling and approximating a waveform by a linear combination of basis functions containing a variable parameter is considered. It is shown that the Kalman equation error concept of linear system identification theory can, in a modified form, be applied to a large class of modeling problems, provided the chosen basis function is a solution of a linear.functional equation in Hilbert space. This class includes rational and Tauberian modeling problems, known to be of relevance for electromagnetic transient response and wide bandwidth radar return signature identification respectively.

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