Model based parameter estimation as a model abstraction technique

In this paper it is demonstrated that the technique of model based parameter estimation (MBPE), specifically Cauchy´s method, can be used in the frequency domain to extrapolate/interpolate a narrowband set of system data or information to a broadband set of data or information. The information can be either computed data or measured experimental data over a frequency band. For computed data the sampled values of the function and a few derivative values are used to reconstruct the function. For measured data only sampled values of the function are used as derivative values are too noisy. Cauchy´s method is based on applying the principle of analytic continuation to a complex, hard to specify function, analytic except at isolated poles, that represents the frequency domain property of interest. Such a function can be represented by a ratio of two polynomials, a reduced order model, which can be considered to be a variant of model abstraction. A procedure is outlined for determining the order of the polynomials and their coefficients using the methods of singular value decomposition (SVD) and least squares. The method is applied to a selected set of frequency domain problems to illustrate the accuracy and versatility of the method