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On Multi-Dimensional Systems: Properties of their Transfer Functions
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.ORCID iD: 0000-0001-7269-5241
2016 (English)In: 2016 URSI INTERNATIONAL SYMPOSIUM ON ELECTROMAGNETIC THEORY (EMTS), IEEE, 2016, p. 512-514Conference paper, Published paper (Refereed)
Abstract [en]

A range of interesting electromagnetic systems like antennas, extraordinary transmission and absorbers have been shown to have certain bandwidth limitations given by a family of sum-rules. Common for the systems are that they are passive, linear and time-translational invariant. In this paper we shortly review the extension from one-dimensional passive systems to multi-dimensional systems, aiming towards constraining the system properties. The most well-known case of system constraints follows from multi-dimensional passivity, where a Schwartz-kernel representation theorem maps Borel-measures with a growth condition to the (complexified) Fourier transform of the transfer function. A weaker form of system constraints follow from generalizations of Kramers-Kronig relations. One such approach is a generalized Cauchy-Bochner representations, under Sobolev space limitations on the transform pair. This approach is closely connected to that the support of the transfer function is within an acute cone. Another approach to system transfer constraints is the multi-dimensional Hilbert-transform, often with squareinte-grable function requirements. It is observed that the Cauchy-Bochner representation and the multi-dimensional Hilbert transform yield different representations in higher dimensions although they give the same in one dimension. We end the paper with a few explicit examples of functions that satisfy the constraints.

Place, publisher, year, edition, pages
IEEE, 2016. p. 512-514
Series
URSI International Symposium on Electromagnetic Theory, ISSN 2163-405X
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-200037DOI: 10.1109/URSI-EMTS.2016.7571440ISI: 000389770800146Scopus ID: 2-s2.0-84992124326ISBN: 978-1-5090-2502-2 (print)OAI: oai:DiVA.org:kth-200037DiVA, id: diva2:1068937
Conference
URSI International Symposium on Electromagnetic Theory (EMTS), AUG 14-18, 2016, Espoo, FINLAND
Note

QC 20170126

Available from: 2017-01-26 Created: 2017-01-20 Last updated: 2017-01-26Bibliographically approved

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Jonsson, B. Lars G.

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