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2017 (English)Report (Other academic)
Abstract [en]
A passive approximation problem is formulated where the target function is an arbitrary complex valued continuous function defined on an approximation domain consisting of a closed interval of the real axis. The approximating function is any Herglotz function with a generating measure that is absolutely continuous with Hölder continuous density in an arbitrary neighborhood of the approximation domain. The norm used is induced by any of the standard L^{p}-norms where 1 ≤ p ≤ ∞. The problem of interest is to study the convergence properties of simple Herglotz functions where the generating measures are given by finite B-spline expansions, and where the real part of the approximating functions are obtained via the Hilbert transform. In practice, such approximations are readily obtained as the solution to a finite- dimensional convex optimization problem. A constructive convergence proof is given in the case with linear B-splines, which is valid for all L^{p}-norms with 1 ≤ p ≤ ∞. A number of useful analytical expressions are provided regarding general B-splines and their Hilbert transforms. A typical physical application example is given regarding the passive approximation of a linear system having metamaterial characteristics. Finally, the flexibility of the optimization approach is illustrated with an example concerning the estimation of dielectric material parameters based on given dispersion data.
Publisher
p. 24
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Physics, Waves and Signals
Identifiers
urn:nbn:se:lnu:diva-63878 (URN)
Funder
Swedish Foundation for Strategic Research , AM13-0011
2017-05-182017-05-182017-06-09Bibliographically approved