Chebyshev collocation and Newton-type optimization methods for the inverse problem on nonuniform transmission lines
A frequency-domain inverse problem for the nonuniform LCRG transmission line is considered. The parameters of the nonuniform line are interpolated by Chebyshev polynomials, and the Telegraphers equations are solved by a collocation method using the same polynomials. The interpolation coefficients fo...
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| Veröffentlicht in: | IEEE transactions on microwave theory and techniques 2005-05, Vol.53 (5), p.1561-1568 |
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| container_title | IEEE transactions on microwave theory and techniques |
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| creator | Norgren, M. |
| description | A frequency-domain inverse problem for the nonuniform LCRG transmission line is considered. The parameters of the nonuniform line are interpolated by Chebyshev polynomials, and the Telegraphers equations are solved by a collocation method using the same polynomials. The interpolation coefficients for the unknown parameters are reconstructed by means of Newton-type optimization methods for which the Jacobian matrix has been calculated explicitly. For the reconstruction of one or two parameters, the algorithm is tested on synthetic data, and the necessity to use regularization is discussed. Finally, the algorithm is tested with measured reflection data to reconstruct shunt capacitances with piecewise constant profiles. |
| doi_str_mv | 10.1109/TMTT.2005.847045 |
| format | Article |
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The parameters of the nonuniform line are interpolated by Chebyshev polynomials, and the Telegraphers equations are solved by a collocation method using the same polynomials. The interpolation coefficients for the unknown parameters are reconstructed by means of Newton-type optimization methods for which the Jacobian matrix has been calculated explicitly. For the reconstruction of one or two parameters, the algorithm is tested on synthetic data, and the necessity to use regularization is discussed. Finally, the algorithm is tested with measured reflection data to reconstruct shunt capacitances with piecewise constant profiles.</description><identifier>ISSN: 0018-9480</identifier><identifier>ISSN: 1557-9670</identifier><identifier>EISSN: 1557-9670</identifier><identifier>DOI: 10.1109/TMTT.2005.847045</identifier><identifier>CODEN: IETMAB</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Algorithms ; Applied sciences ; Chebyshev approximation ; Circuit properties ; Collocation ; Distributed parameter circuits ; Electric, optical and optoelectronic circuits ; Electronics ; Equations ; Exact sciences and technology ; frequency-domain ; Interpolation ; inverse problem ; Inverse problems ; Jacobian matrices ; Mathematical analysis ; Microwave circuits, microwave integrated circuits, microwave transmission lines, submillimeter wave circuits ; Nonuniform ; Optimization ; Optimization methods ; Polynomials ; Reconstruction ; simultaneous reconstruction ; Testing ; transmission line ; Transmission line matrix methods ; Transmission lines</subject><ispartof>IEEE transactions on microwave theory and techniques, 2005-05, Vol.53 (5), p.1561-1568</ispartof><rights>2005 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2005</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c420t-b27c6c2ab48b763a8d24e842d015c514848464fa844483f6181c75d8e18a0e283</citedby><cites>FETCH-LOGICAL-c420t-b27c6c2ab48b763a8d24e842d015c514848464fa844483f6181c75d8e18a0e283</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/1427958$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>230,314,780,784,796,885,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/1427958$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16771703$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-14741$$DView record from Swedish Publication Index$$Hfree_for_read</backlink></links><search><creatorcontrib>Norgren, M.</creatorcontrib><title>Chebyshev collocation and Newton-type optimization methods for the inverse problem on nonuniform transmission lines</title><title>IEEE transactions on microwave theory and techniques</title><addtitle>TMTT</addtitle><description>A frequency-domain inverse problem for the nonuniform LCRG transmission line is considered. The parameters of the nonuniform line are interpolated by Chebyshev polynomials, and the Telegraphers equations are solved by a collocation method using the same polynomials. The interpolation coefficients for the unknown parameters are reconstructed by means of Newton-type optimization methods for which the Jacobian matrix has been calculated explicitly. For the reconstruction of one or two parameters, the algorithm is tested on synthetic data, and the necessity to use regularization is discussed. Finally, the algorithm is tested with measured reflection data to reconstruct shunt capacitances with piecewise constant profiles.</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Chebyshev approximation</subject><subject>Circuit properties</subject><subject>Collocation</subject><subject>Distributed parameter circuits</subject><subject>Electric, optical and optoelectronic circuits</subject><subject>Electronics</subject><subject>Equations</subject><subject>Exact sciences and technology</subject><subject>frequency-domain</subject><subject>Interpolation</subject><subject>inverse problem</subject><subject>Inverse problems</subject><subject>Jacobian matrices</subject><subject>Mathematical analysis</subject><subject>Microwave circuits, microwave integrated circuits, microwave transmission lines, submillimeter wave circuits</subject><subject>Nonuniform</subject><subject>Optimization</subject><subject>Optimization methods</subject><subject>Polynomials</subject><subject>Reconstruction</subject><subject>simultaneous reconstruction</subject><subject>Testing</subject><subject>transmission line</subject><subject>Transmission line matrix methods</subject><subject>Transmission lines</subject><issn>0018-9480</issn><issn>1557-9670</issn><issn>1557-9670</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kUGP1SAUhRujic_RvYkbYqKzsU-gUOhy8nTUZNTN0y2h9NYytlCBzuT566XpxElcGBaE3O-cnMspiucE7wnBzdvj5-NxTzHme8kEZvxBsSOci7KpBX5Y7DAmsmyYxI-LJzFe5yfjWO6KeBigPcUBbpDx4-iNTtY7pF2HvsBt8q5MpxmQn5Od7O9tOEEafBdR7wNKAyDrbiBEQHPw7QgTyojzbnE2AxNKQbs42RhX6WgdxKfFo16PEZ7d3WfFt8v3x8PH8urrh0-Hi6vSMIpT2VJhakN1y2Qr6krLjjKQjHaYcMMJk_nUrNeSMSarviaSGME7CURqDFRWZ8WbzTfewry0ag520uGkvLbqnf1-oXz4oX6mQREmGMn4-YbnPX4tEJPKqQ2Mo3bgl6hkU1PKRUMz-fq_JJUYM8ZXy5f_gNd-CS4vrWQtcnpZ8QzhDTLBxxig_xuUYLV2q9Zu1dqt2rrNkld3vjoaPfb5i42N97paCCJwlbkXG2cB4H7MqGi4rP4AAvSuUw</recordid><startdate>20050501</startdate><enddate>20050501</enddate><creator>Norgren, M.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>8FD</scope><scope>L7M</scope><scope>F28</scope><scope>FR3</scope><scope>ADTPV</scope><scope>AOWAS</scope><scope>D8V</scope></search><sort><creationdate>20050501</creationdate><title>Chebyshev collocation and Newton-type optimization methods for the inverse problem on nonuniform transmission lines</title><author>Norgren, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c420t-b27c6c2ab48b763a8d24e842d015c514848464fa844483f6181c75d8e18a0e283</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Chebyshev approximation</topic><topic>Circuit properties</topic><topic>Collocation</topic><topic>Distributed parameter circuits</topic><topic>Electric, optical and optoelectronic circuits</topic><topic>Electronics</topic><topic>Equations</topic><topic>Exact sciences and technology</topic><topic>frequency-domain</topic><topic>Interpolation</topic><topic>inverse problem</topic><topic>Inverse problems</topic><topic>Jacobian matrices</topic><topic>Mathematical analysis</topic><topic>Microwave circuits, microwave integrated circuits, microwave transmission lines, submillimeter wave circuits</topic><topic>Nonuniform</topic><topic>Optimization</topic><topic>Optimization methods</topic><topic>Polynomials</topic><topic>Reconstruction</topic><topic>simultaneous reconstruction</topic><topic>Testing</topic><topic>transmission line</topic><topic>Transmission line matrix methods</topic><topic>Transmission lines</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Norgren, M.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>SwePub</collection><collection>SwePub Articles</collection><collection>SWEPUB Kungliga Tekniska Högskolan</collection><jtitle>IEEE transactions on microwave theory and techniques</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Norgren, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Chebyshev collocation and Newton-type optimization methods for the inverse problem on nonuniform transmission lines</atitle><jtitle>IEEE transactions on microwave theory and techniques</jtitle><stitle>TMTT</stitle><date>2005-05-01</date><risdate>2005</risdate><volume>53</volume><issue>5</issue><spage>1561</spage><epage>1568</epage><pages>1561-1568</pages><issn>0018-9480</issn><issn>1557-9670</issn><eissn>1557-9670</eissn><coden>IETMAB</coden><abstract>A frequency-domain inverse problem for the nonuniform LCRG transmission line is considered. The parameters of the nonuniform line are interpolated by Chebyshev polynomials, and the Telegraphers equations are solved by a collocation method using the same polynomials. The interpolation coefficients for the unknown parameters are reconstructed by means of Newton-type optimization methods for which the Jacobian matrix has been calculated explicitly. For the reconstruction of one or two parameters, the algorithm is tested on synthetic data, and the necessity to use regularization is discussed. Finally, the algorithm is tested with measured reflection data to reconstruct shunt capacitances with piecewise constant profiles.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TMTT.2005.847045</doi><tpages>8</tpages></addata></record> |
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| subjects | Algorithms Applied sciences Chebyshev approximation Circuit properties Collocation Distributed parameter circuits Electric, optical and optoelectronic circuits Electronics Equations Exact sciences and technology frequency-domain Interpolation inverse problem Inverse problems Jacobian matrices Mathematical analysis Microwave circuits, microwave integrated circuits, microwave transmission lines, submillimeter wave circuits Nonuniform Optimization Optimization methods Polynomials Reconstruction simultaneous reconstruction Testing transmission line Transmission line matrix methods Transmission lines |
| title | Chebyshev collocation and Newton-type optimization methods for the inverse problem on nonuniform transmission lines |
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