Using adaptive sampling to minimize the number of samples needed to represent a transfer function

One of the most commonly encountered problems in wave-equation applications such as arise in acoustics and electromagnetics is that of estimating transfer functions from discrete frequency samples of a first-principles, or generating model (GM) such as NEC, FERM, E-PATCH, etc. This problem has been approached in a mostly ad hoc way wherein the GM samples are spaced uniformly and closely enough such that linear interpolation yields a reasonably smooth graphical representation of the continuous response. Often, additional sampling between the original ones is done subsequently to improve the result, a process that may be repeated several times until an apparently satisfactory outcome is obtained. This approach will usually result in substantial oversampling, with a concomitant increase in the associated cost, while offering no assurance that important details of the true GM transfer function have not been missed. At the same time, there is no quantitative measure of how much the linearly interpolated estimate might differ from the actual response between the sampled values. The procedure described uses model-based parameter estimation with rational-function, overlapping fitting models (FMs) to automatically determine where the GM needs to be sampled to reduce the mismatch between the FMs, and their estimate of the GM, below a specified value.